European Mathematical Society - 57 Manifolds and cell complexes
https://euro-math-soc.eu/msc/57-manifolds-and-cell-complexes
enA Guide to the Classification Theorem of Compact Surfaces
https://euro-math-soc.eu/review/guide-classification-theorem-compact-surfaces
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>Undoubtedly, one of the most beautiful pieces of the mathematical achievements is the classification of compact surfaces. Among other reasons, the result comprises a splendid combinatin of intuition and rigour as well as the extensive use of many geometric and (mainly) topological tools. In addition, this milestone has been the starting point of many essential contemporary mathematical works.</p>
<p>The book under review tackles this central topic. The classification theorem can be found in many excellent classical monographs, mainly as a part of a course on Algebraic Topology, with different approaches and depth. Under this panorama, the motivation of this book is the presentation of the classification theorem as an only topic, giving the required importance to all its view points: intuition, visualization, topological tools, history,… amenable to a wide audience with certain amount of mathematical maturity.</p>
<p>The book is structured in six chapters, guiding the reader from the presentation and intuition of the problema to the complete proof of it. Each chapter provides a good list of references connnecting its topic to the literature. At the end, some appendices complete the work, the history of the classification problem being specially interesting.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Marco Castrillon Lopez</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book tackles the classical result of the Theorem of Classification of compact surfaces, starting from the intuition and ending with a rigorous and complete proof.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/jean-gallier" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Jean Gallier</a></li><li class="vocabulary-links field-item odd"><a href="/author/dianna-xu" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Dianna Xu</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/springer-verlag" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">springer-verlag</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2013</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-3-642-34363-6</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">178</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/geometry" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Geometry</a></li><li class="vocabulary-links field-item odd"><a href="/imu/topology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Topology</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.springer.com/la/book/9783642343636" title="Link to web page">http://www.springer.com/la/book/9783642343636</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/57-manifolds-and-cell-complexes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57 Manifolds and cell complexes</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/57-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57-01</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/57n05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57N05</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/57m20" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57M20</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/55-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">55-01</a></li></ul></span>Sat, 27 Jan 2018 16:17:28 +0000Marco Castrillon Lopez48208 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/guide-classification-theorem-compact-surfaces#commentsA primer on mapping class groups
https://euro-math-soc.eu/review/primer-mapping-class-groups
<div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Raquel Díaz, Álvaro Martínez</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad Complutense de Madrid, Universidad de Castilla la Mancha</div></div></div><div class="field field-name-field-review-appendix field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://euro-math-soc.eu/sites/default/files/reviewMCG.pdf" type="application/pdf; length=84390" title="reviewMCG.pdf">A primer on mapping class groups</a></span></div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book is a first course in mapping class groups. It presents a wide variety of results of this beautiful theory which lies in the intersection of geometry, topology and group theory. It is suitable for graduate students and researches interested in this area.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/benson-farb" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">benson farb</a></li><li class="vocabulary-links field-item odd"><a href="/author/dan-margalit" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">dan margalit</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2011</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-691-14794-9</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/57-manifolds-and-cell-complexes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57 Manifolds and cell complexes</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/57m50" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57m50</a></li></ul></span>Thu, 18 Apr 2013 12:10:03 +0000Anonymous45502 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/primer-mapping-class-groups#commentsVirtual knots. The State of the Art
https://euro-math-soc.eu/review/virtual-knots-state-art
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>The study of knots and their properties is known as knot theory. Classical theory counts more than two hundred and fifty years. Knots appear in Chinese knotting, Tibetan Buddhism, intricate Celtic knot-work, in the 1200 year old Book of Kells, and so on. As a mathematical theory appeared in 1771 by French mathematician Vandermonde, when discussing the properties of knots related to the geometry of position. Mathematical studies of knots began in the 19th century with Gauss, who defined the linking integral. This theory was given its first impetus when Lord Kelvin proposed a theory that atoms were vortex loops, with different chemical elements consisting of different knotted configurations, P.G. Tait then cataloged possible loops with different knots by trial and error, the first knot tables with up to ten crossings, known as the Tait conjectures, this record motivated that knot theory became part of the emerging subject of topology. Over six billion knots and links have been tabulated since the beginnings of knot theory in the 19th century. Much progress has been made in the intervening years, for example, Alexander, Dehn, Klein, Reidemeister, and other outstanding mathematicians. </p>
<p>A knot is defined as a closed non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., unknot). To a mathematician, an object is a knot only if its free ends are attached in some way so that the resulting structure consists of a single looped strand. A knot can be generalized to a link which is simply a knotted collection of one o more closed strands. A virtual knot represents a natural combinatorial generalization of a classical knot, simply introduced a new type of a crossing and extended new moves to the list of the Reidemester moves, the new crossing (virtual) should be treated as a diagrammatic picture of two part of a knot (a link) on the plane which are far from each other, and the intersection of these parts is artifact of such a drawing. In short, a virtual diagram (or a diagram of a virtual link) is the image of an inmersion of a framed 4-valent graph in R2 with a finite number of intersections of edges. Moreover, each intersection is a transverse double point which named a virtual crossing and mark by a small circle, and each vertex of the graph is endowed, with the classical crossing structure. The theory of knots in three-dimensional Euclidean space or in the three-sphere (the classical theory) is an integral part of a much larger theory, knots in 3-manifolds. </p>
<p>This remarkable book is the first systematic and full-length book on the theory of virtual knots and links, devoted to an intriguing and comprehensive study of (virtual and classical) knots as integral part. The book is self-contained. The mathematical material is sufficiently closed, and contains up-to-date exposition of the key aspect of virtual (and classical) knot theory. The book is quite accessible for undergraduate students of low courses, thus it can be used as a basic course book on virtual and classical knot theory. This book can also be useful for professionals and amateur mathematicians because it contains the newest and the most significant scientific developments in knot theory. The book was written using knots.tex fonts containing special symbols from knot Theory.</p>
<p>The aim of the present book is to describe the main concepts of modern knot theory together with full proofs that would be both accessible to beginners and useful for professionals. A large part of the present title is devoted to rapidly developing areas of modern knot theory: such as virtual knot theory and Legendrian knot theory.</p>
<p>Over the last decades, knot theory was enriched by numerous methods and subtle invariants, which today constitute a powerful tool in knot theory and low-dimensional topology. A breakthrough in knot theory is due to discoveries of Conway, Jones and Vassiliev (Conway and Jones polynomials, Vassiliev´s finite type invariants). For their impact to knot theory which related knot theory to various branches of mathematics and physics, Jones, Witten, Drinfeld (1990) y Kontsevich(1998) were awarded the highest honor of mathematics, The Fields medals.</p>
<p>Virtual knots were discovered by Louis H. Kauffman, in 1996, and independently by Goussarov, Polyak and Viro in 2000, about finite type invariants of classical and virtual knots. The first paper on virtual knot theory appeared in 1999, by Louis H. Kauffman in European Journal of Combinatory. The virtual knot theory helped one to understand better some aspects of the classical knot theory. By means of virtual knot theory, the problem of existence of combinatorial formulae for finite type invariants for classical knots was solved. </p>
<p>A common point of view allows us to treat classical and virtual knots uniformly.</p>
<p>A classical knot (link) can be given by a planar diagram. There are classical crossings and curves connecting crossings to each other. In the classical knot is possible that the curves connecting crossings can be chosen to be non-intersecting and in some cases it is impossible to situate these curves without additional intersections. This new intersections are marked as virtual (encircled) and we get a virtual diagram. Virtual crossings appear every time, when a 4-valent graph defined by classical crossings and ways of connection, is not planar, which happens quite often.</p>
<p>Thus, virtual knots are related to classical knots approximately in the same way as graphs are related to planar graphs. Herewith, the equivalence (isotopy) of classical knot diagrams is defined by means of formal combinatorial transformations (Reidemeister moves), which are applied to crossing lying close to each other.</p>
<p>From the topological point of view, the virtual knots are knots in thickened surfaces (products of sphere with handles with an interval) considered up to isotopy and stabilizations. </p>
<p>The book contains nine chapters, bibliography and an index, in 520 pp. It goes from the basics to the frontiers of research. The book is volume 51 of Series on Knots and Everything, polarized around the theory of Knot Theory. The questions treated reach out beyond theory itself into physics, mathematics, logic, linguistics, philosophy, biology and practical experienced. The book is dedicated to the memory of Oleg Vassilievich Manturov (1936-2011), father of Vassily Olegovich Manturov, first-named author of the book. </p>
<p>The first chapter, untitled basic, definitions and notions, devoted to the diagrammatic and combinatorial definitions and to a discovery of the self-linking number of a virtual knot. This chapter is a compendium, remarkable and fascinating encyclopedic treatment of basics. </p>
<p>In Chapter 2, is dedicated to virtual knots and the three dimensional topology. The authors present a discussion of Kuperberger´s Theorem, and the surface genus of virtual knots. Kuperberger proved that if a virtual knot (link) is represented in its minimal genus surface, then this embedding type is unique. The result is interesting because is fruitful for getting deeper invariants, a stronger version of the Jones polynomial for virtual knots and links. This chapter also proves that virtual knots are algorithmically recognizable by generalizing the technique of Haken and Hemion for classical knots. The recognition problem for classical knots was one of the central problems in low-dimensional topology. Its first solution is related to Haken´s normal surface theory, and the final steps belong to Matveev. The result of algorithmic recognizability of a certain object in low-dimensional topology is important, because, in low-dimensional topology, the algorithmic non-realizability takes place for many objects. When virtual knot theory appeared, the problem of algorithmic realizability of virtual knots arose. This problem is resolved positively, in this chapter. This result relies not only on Haken´s theory, but also on Kuperberg´s theorem.</p>
<p>In chapter 3 on consider quandles (distributive groupoids) and their generalizations to virtual knots. Generalizations of invariants that emerged, from virtual knot theory, is the use of the biquandle, and its powerful applications to the theory. Biquandle is a generalization of the quandle, which in turn generalizes the fundamental group of a knot (link). It worth the Lie algebraic techniques for invariants, long virtual knots, and the hierarchy of virtual knots, where have ordered by some choice of an ordinal, in terms of their ability to move across one another. Some invariants are found here by the hierarchy of virtual knots.</p>
<p>Chapter 4 does the basics of the Jones-Kauffman polynomials via the bracket state sum and introduces the concept of atoms (surfaces, orientable or not, bearing the virtual knot diagram). It also treated the chord diagrams and the passage from atoms to chord diagrams. The spanning tree, the leading and lowest terms of the Kauffman bracket polynomial, Kauffman bracket for rigid knots, and so on. It ends with the study of minimal diagrams of long virtual knots. </p>
<p>In Chapter 5, in the present book, on dealing with many ideas related to virtual theory can be directed to the study of Khovanov homology, as the homology of an algebraic complex which is constructed with a diagram of a knot (link), this homology detects the unknot, which seriously enlarges horizons of the theory. The Khovanov theory, associates with each knot diagram a chain complex, whose homology is a knot invariant, and the Euler characteristic of this complex coincides with the Jones polynomial. These chains constructed with a knot diagram, correspond to formal smoothing of this diagram at all classical crossings. It is interesting that the differentials of the Khovanov complex are defined combinatorially, and the homology is invariant under Reidemeister moves. To extend Khovanov homology theory to virtual knots, Manturov had to revisit completely the theory and construct a complex homotopically equivalent to the usual Khovanov complex. The problem, in the case of virtual knots, is related to the well definedness in order for the square of the differential to be equal to zero. This procedure needs to be computed, and compared with the Khovanov Rozansky Categorified Link Homology. A key role in this construction was played by the notion of atom and played a crucial role in the proof of Vassiliev´s conjecture. Such construction is very nice because required a number of new ideas: orientation and enumeration of the state curves; twisted coefficients in the Frobenius algebra representing, and the usage of exterior products instead of usual products. In short, the authors gave a first combinatorial solution to the question of constructing integral Khovanov homology for the virtual knots and links.</p>
<p>Chapter 6 deals with virtual braids and the work of Kamada (2007), and Kauffman and Lambropoulou(2006), and the considerations of the invariants of virtual braids, in the following cases, the construction of the main invariant, then the representation of virtual braid group. On the other hand, studies on completeness in the classical case and the case of two-strand braids.</p>
<p>Chapter 7 treats combinatorial aspects of the Vassieliev invariant theory and the work of Goussarov, Polyak and Viro who used virtual knots in the guise of general Gauss diagrams to construct a theory of Gauss diagram formulas for virtual knots. Virtual knot theory, its constructions and methods are closely related to various branches of classical knot theory, in particular, to Vassiliev invariants. These occupy a special position in classical knot theory; it turned out just, when this theory appeared, that all polynomial and quantum invariants were expressible in terms of Vassiliev invariants. In the case of virtual knots, the theory of Vassiliev knot invariants is much more complicated; even the space of order zero invariants is infinite-dimensional. In this chapter, by using atoms and d-diagrams, on proved Vassiliev´s conjecture about planarity of framed 4.valent graphs (graphs where at each vertex four half-edges are split into two pairs of opposite ones); this conjecture solved positively, plays a key role in Vassiliev´s work on the existence of integer-valued combinatorial formulae for invariants of finite order.</p>
<p>The chapter 8 is devoted to parity in knot theory. In virtual knot theory, there are many unexpected invariants which do not take place in the classical case. This chapter includes work on the Goldman bracket, and the Turaev cobracter and on cobordism of free knots. At first it was thought (a conjecture of Turaev) that free knots were trivial, but the most striking example of such theory is the parity theory conceived by Vassily Olegovich Manturov, where all classical crossings are either even or odd, herewith the property of being even is naturally preserve by Reidemeister moves. By parity, we mean any such natural way of labeling of all classical crossing which is defines for all knots from this theory. Manturov showed, using parity that this is not the case and that there are non-trivial cobordism classes of free knots. By means of parity, one can construct functorial mappings from knots to knots, filtrations on the space of knots, refine many invariants and prove minimality of many series of knot diagrams. The analogous virtual knot theory is to study virtual knots up to change of orientation of the crossings as we describe of the beginnings, to study virtual knots up to virtualization equivalence. The existence of different parities and different projections (from knots to knots) allows one to establish various filtrations on the space of knots. Besides that, such projections allows, one to lift invariants, from classical knots to virtual knots.</p>
<p>Finally the Chapter 9 on Graph link theory, a further combinatorial. The passage from classical knots to virtual knots can also be motivated by representing Reidemeister moves in the language of Gauss diagrams. Every Gauss diagram is a circle with a collection of pairs of points (all points mutually disjoint); every pair of points is endowed with an arrow from one point to the other and a sign. Each chord diagram of such sort has an intersection graph. Vertices of the intersection graph correspond to the chords, and two vertices are adjacent whenever the corresponding chords are linked. To such graphs, one can extend Reidemeister moves. Note that not all simple (without multiple edges and loops) graphs originate from chord diagrams. When passing from intersection graphs of chord diagrams to arbitrary graphs and extending Reidemeister moves to such graphs, we end up with the graph-link theory due to the authors of the present book. An analogous theory was constructed by Traldi and Zulli. Graph link can be treated as diagramless knot theory. Such links have crossing, but they do not have arcs connecting this crossings since the corresponding graphs are not intersection graphs of any chord diagrams and thus they are not drawable on the plane. It turns out, however, that to graph-links one can extend many methods of the classical and virtual knot theory, in particular, the parity theory. We have constructed various invariants, proved the equivalence of two approaches to graph-knots: the one suggested by the authors and the one suggested by Traldi and Zulli. We have constructed various invariants showing non-realizability of graph-links (the fact that a graph-link has no drawable representative). A remarkable achievement in the graph-link theory is the work by Nikonov, who constructed Khovanov homology theory for graph-links with coefficients from Z2. Unlike the usual Kauffman bracket when one had to count the number of non-existing state-circles, for this problem one had to understand how these non-existing circles might interfere in order to construct the differential in the Khovanov complex.</p>
<p>The theories mentioned above are related to different problems of combinatorics, three-dimensional topology, and four-dimensional topology, representation theory for Lie groups and algebras. Representation theory is the starting point for constructing quantum invariants of knots and 3- manifolds.</p>
<p>The book is the result of the research for over 10 years, different questions of virtual knot theory were discussed in the seminar “Knots and the representation theory” and Seminar on “Tensor and Vector Analysis” (the latter exists since 1920s) in the Moscow State University.</p>
<p>Definitely the book is high recommended to undergraduate, graduate, professionals and amateur mathematicians, because it goes from the basics to the frontiers of research. Finally, as L.H. Kauffman says: “this book self-contained is motivated, to delve, into the adventure proposed, by this intriguing and remarkable book”.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Francisco José Cano Sevilla</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Profesor Universidad Complutense</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book is the first systematic and full-length book on the theory of virtual knots and links, devoted to an intriguing and comprehensive study of (virtual and classical) knots as integral part. The book is self-contained. The mathematical material is sufficiently closed, and contains up-to-date exposition of the key aspect of virtual (and classical) knot theory. The book is quite accessible for undergraduate students of low courses, thus it can be used as a basic course book on virtual and classical knot theory.<br />
The aim of the present book is to describe the main concepts of modern knot theory together with full proofs that would be both accessible to beginners and useful for professionals. A large part of the present title is devoted to rapidly developing areas of modern knot theory: such as virtual knot theory and Legendrian knot theory.<br />
The book contains nine chapters, bibliography and an index, in 520 pp. It goes from the basics to the frontiers of research. The book is volume 51 of Series on Knots and Everything, polarized around the theory of Knot Theory. The questions treated reach out beyond theory itself into physics, mathematics, logic, linguistics, philosophy, biology and practical experienced. The book is dedicated to the memory of Oleg Vassilievich Manturov (1936-2011), father of Vassily Olegovich Manturov, first-named author of the book.</p>
<p>Definitely the book is high recommended to undergraduate, graduate, professionals and amateur mathematicians, because it goes from the basics to the frontiers of research. Finally, as L.H. Kauffman says: “this book self-contained is motivated, to delve, into the adventure proposed, by this intriguing and remarkable book”.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/vassily-olegovich-manturov" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">vassily olegovich manturov</a></li><li class="vocabulary-links field-item odd"><a href="/author/denis-petrovich-ilyutko" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">denis petrovich ilyutko.</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/new-jersey-world-scientific-publishing-co-pte-ltd-series-knots-and-everything-vol-51" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">new jersey. world scientific publishing co. pte. ltd. series on knots and everything: vol. 51.</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2012</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">ISBN-13: 978-981-4401-12-8; ISBN 10:9814401129; ISSN 0219-9769</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">168$(Hardcover: alk. paper), 91.05$ (kindle Edit)</div></div></div><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/www.worldscientific.com" title="Link to web page">www.worldscientific.com</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/57-manifolds-and-cell-complexes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57 Manifolds and cell complexes</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/57m27-57m25-57q45" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57m27, 57m25, 57q45</a></li></ul></span>Mon, 01 Apr 2013 09:14:48 +0000Anonymous45497 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/virtual-knots-state-art#commentsElements of Combinatorial and Differential Topology
https://euro-math-soc.eu/review/elements-combinatorial-and-differential-topology
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>The main topic of this book is combinatorial and differential topology. The author discusses a lot of interesting and basic facts avoiding sophisticated techniques, hence the reading of the book requires only a modest background for these topics (e.g. basic topological properties of sets in Euclidean space). After an introductory discussion of graphs, the topology of subsets in Euclidean space is considered (including the Jordan theorem for curves, the Brouwer fixed point theorem and the Sperner lemma). Simplicial complexes and CW-complexes are discussed in the next chapter, followed by a treatment of surfaces, coverings, fibrations and homotopy groups. The fifth chapter turns to differential topology (smooth manifolds, embeddings and immersions, the degree of a map, the Hopf theorem on the homotopy classification of maps to the sphere and Morse theory). The last chapter treats the fundamental groups (with many explicit examples). The book contains a lot of problems and their solutions can be found at the end of the book.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">vs</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/v-v-prasolov" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">v. v. prasolov</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/american-mathematical-society-providence-graduate-studies-mathematics-vol-74" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society, providence: graduate studies in mathematics, vol. 74</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2006</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">0-8218-3809-1 </div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">USD 59</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/57-manifolds-and-cell-complexes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57 Manifolds and cell complexes</a></li></ul></span>Sun, 23 Oct 2011 18:19:49 +0000Anonymous40082 at https://euro-math-soc.euDifferential Geometry and Topology - With a View to Dynamical Systems
https://euro-math-soc.eu/review/differential-geometry-and-topology-view-dynamical-systems
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book offers a nice introduction to major topics in differential geometry and differential topology and their applications in the theory of dynamical systems. It starts with a chapter on manifolds (including the Sard theorem), followed by a discussion of vector fields, the Lie derivative and Lie brackets, and discrete and smooth dynamical systems. The following chapters treat Riemannian manifolds, affine and Levi-Civita connections, geodesics, curvatures, Jacobi fields and conjugate points and the geodesic flow. The chapter on tensors and differential forms includes integration of differential forms, Stokes theorem and a discussion of the de Rham and singular homology. Chapter 7 contains a description of the Brouwer degree, intersection numbers, Euler characteristics, and the Gauss-Bonnet theorem. Chapter 8 treats Morse theory and the final chapter discusses hyperbolic dynamical systems and geodesic flows. The book is nicely written and understandable, with many illustrations and intuitive comments. It is very suitable as an introduction to the field.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">vs</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/k-burns" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">k. burns</a></li><li class="vocabulary-links field-item odd"><a href="/author/m-gidea" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">m. gidea</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/chapman-hallcrc-boca-raton-studies-advanced-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">chapman & hall/crc, boca raton: studies in advanced mathematics</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2005</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">1-58488-253-0</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">USD 89,95</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/57-manifolds-and-cell-complexes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57 Manifolds and cell complexes</a></li></ul></span>Fri, 21 Oct 2011 17:29:00 +0000Anonymous39941 at https://euro-math-soc.euSurfaces in 4-Space
https://euro-math-soc.eu/review/surfaces-4-space
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>The new volume of the long term project Encyclopaedia of Mathematical Sciences belongs to the sub-series ‘Low-dimensional topology’. The topic described in the book is topology of surfaces in four dimensions. The first chapter describes various diagrammatic methods (motion pictures, normal forms, marked vertex diagrams, surface braids, etc.) and their relations. Constructions of knotted surfaces are discussed in the second chapter. The third chapter introduces a lot of invariants for knotted surfaces. A quandle is a set with a self-distributive binary operation. The quandle cocycle invariants are discussed in the last chapter of the book. There is also a geometric interpretation of quandle homology using coloured cobordisms. Twenty-five pages of quandles and their homology groups are available in the appendix. Ten pages of references are also included. Even though drawings of surfaces in four-dimensional space are impossible, the book is richly illustrated by many drawings and diagrams.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">vs</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/s-carter" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">s. carter</a></li><li class="vocabulary-links field-item odd"><a href="/author/s-kamada" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">s. kamada</a></li><li class="vocabulary-links field-item even"><a href="/author/m-saito" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">m. saito</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/springer-berlin-encyclopaedia-mathematical-sciences-vol-142" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">springer, berlin: encyclopaedia of mathematical sciences, vol. 142</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2004</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">3-540-21040-7</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">EUR 84,95</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/57-manifolds-and-cell-complexes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57 Manifolds and cell complexes</a></li></ul></span>Fri, 30 Sep 2011 11:21:20 +0000Anonymous39749 at https://euro-math-soc.euThe Reidemeister Torsion of 3-Manifolds
https://euro-math-soc.eu/review/reidemeister-torsion-3-manifolds
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This is a book on the Reidemeister torsion and its (mostly Turaev’s) generalizations. When comparing it with Turaev’s book (Introduction to Combinatorial Torsions, Lectures in Mathematics, ETH Zürich, Birkhäuser, 2001), which appeared recently, we can immediately see that it has a different character. While Turaev’s book can also serve as a kind of introduction to the subject (as well as an introduction to the contemporary research in the field), the book under review is devoted to a wide range of applications of the torsion, and its reading requires certain prerequisites. In the first chapter, which makes the reader familiar with the necessary algebraic notions, the reader is supposed to have some topological (and also algebraic) background. The author modestly states in the introduction that this is a computationally oriented little book. But let us note that the “computations” we find here are very clever computations, and the wide variety of applications presented here do not support the description of a little book. The book will be indispensable for specialists in the field, and I think that it is very good that it exists together with Turaev’s book. It is very well written, with many examples and also many exercises. The wide range of applications will be interesting not only for topologists but also for differential geometers.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">jiva</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/l-i-nicolaescu" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">l. i. nicolaescu</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/walter-de-gruyter" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">walter de gruyter</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2003</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">3-11-017383-2</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">€84</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/57-manifolds-and-cell-complexes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57 Manifolds and cell complexes</a></li></ul></span>Mon, 12 Sep 2011 14:31:13 +0000Anonymous39687 at https://euro-math-soc.euFoliations II
https://euro-math-soc.eu/review/foliations-ii
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This is the second volume of the two-volume series with the title Foliations. It has three independent parts, describing three special topics in the theory of foliations: Analysis on foliated spaces, Characteristic classes of foliations and Foliated 3-manifolds. Each part contains a description of a topic in foliation theory and its relation to another field of contemporary mathematics. In the first part, the C*- algebras of foliated spaces are studied and some of the classical notions from Riemannian geometry (heat flow and Brownian motion) are generalized to foliated spaces. Necessary analytic background can be found in three appendices. The second part is devoted to characteristic classes and foliations. Here the reader can find constructions of exotic classes based on the Chern-Weil theorem, vanishing theorem for Godbillon-Vey classes and a discussion on obstructions to existence of a foliation transverse to the fibres of circle bundles over surfaces. In the third part, compact 3-manifolds foliated by surfaces are studied. Special methods of 3-manifolds topology yield existence theorems and further results unique for dimension three. There is an appendix with a proof and further discussion of Palmeiras theorem, which says that the only simply connected n-manifold foliated by leaves diffeomorphic to Rn-1 is Rn. The book contains a lot of interesting results and can be recommended to anybody interested in the topic.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">jbu</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/candel" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">a. candel</a></li><li class="vocabulary-links field-item odd"><a href="/author/l-conlon" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">l. conlon</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2003</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">0-8218-0809-5</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">$79</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/57-manifolds-and-cell-complexes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57 Manifolds and cell complexes</a></li></ul></span>Mon, 12 Sep 2011 13:14:48 +0000Anonymous39665 at https://euro-math-soc.euThree-dimensional Orbifolds and Their Geometric Structures
https://euro-math-soc.eu/review/three-dimensional-orbifolds-and-their-geometric-structures
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>A classical result in two dimensions says that a compact surface is diffeomorphic to the quotient of one of three model geometries (the sphere, the Euclidean plane and the hyperbolic plane) by a discrete subgroup of the group of all isometries. In three dimensions, there are eight model geometries. The Thurston geometrization conjecture claims, roughly speaking, that any compact three-dimensional manifold is uniquely decomposable along a finite set of embedded surfaces into quotients of model three-dimensional geometries. It results in a few other important conjectures (including the famous Poincaré conjecture). Studying quotients of manifolds by discrete subgroups, it is natural to work in a broader category of orbifolds. The main aim of the book is to describe this circle of ideas. The authors discuss in turn homogeneous 3-dimensional geometries, canonical decompositions, Haken orbifolds, Seifert fibered orbifolds, the Thurston hyperbolization theorem, varieties of representations, hyperbolic Dehn filling for orbifolds and the orbifold theorem. The Perelman results based on different techniques (the Ricci flow equation) are not included. The book is well organized and nicely written.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">vs</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/m-boileau" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">m. boileau</a></li><li class="vocabulary-links field-item odd"><a href="/author/s-maillot" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">s. maillot</a></li><li class="vocabulary-links field-item even"><a href="/author/j-porti" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">j. porti</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/soci%C3%A9t%C3%A9-math%C3%A9matique-de-france-paris" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">société mathématique de france, paris</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2003</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">2-85629-152-X </div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">25 EUR</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/57-manifolds-and-cell-complexes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57 Manifolds and cell complexes</a></li></ul></span>Thu, 16 Jun 2011 19:31:52 +0000Anonymous39584 at https://euro-math-soc.euGeometrization of 3-Orbifolds of Cyclic Type
https://euro-math-soc.eu/review/geometrization-3-orbifolds-cyclic-type
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This research monograph is devoted to the geometry and topology of 3-dimensional manifolds (or, more generally, 3-dimensional orbifolds). This field was enormously influenced and advanced by work of W. Thurston, and the authors give a full proof of the Thurston orbifold theorem in the case where all local isotropy groups are cyclic subgroups of SO(3). As a consequence, they can prove the Thurston geometrisation conjecture for compact orientable irreducible 3-manifolds with a non-free symmetry. The first appendix is written in collaboration with M. Heusner.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">vs</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/m-boileau" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">m. boileau</a></li><li class="vocabulary-links field-item odd"><a href="/author/j-porti" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">j. porti</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/soci%C3%A9t%C3%A9-math%C3%A9matique-de-france" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">société mathématique de france</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2001</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">2-85629-100-7</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">FRF 250</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/57-manifolds-and-cell-complexes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">57 Manifolds and cell complexes</a></li></ul></span>Wed, 15 Jun 2011 20:38:19 +0000Anonymous39521 at https://euro-math-soc.eu