European Mathematical Society  f. kirwan
https://euromathsoc.eu/author/fkirwan
en

An Introduction to Intersection Homology Theory, second edition
https://euromathsoc.eu/review/introductionintersectionhomologytheorysecondedition
<div class="field fieldnamefieldreviewreview fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem even"><div class="tex2jax"><p>This book represents the second edition of the book of the same title but only one author, namely F. Kirwan. It appeared as volume 187 in the Pitman Research Notes in Mathematical Sciences (Longman Scientific & Technical, Harlow) in 1988. For this second edition another author was asked to cooperate with F. Kirwan and the text has been substantially extended. The original idea of the first author was to explain intersection homology and provide the reader with the proof (or at least a sketch of the proof) of the KazhdanLusztig conjecture. The book in the present form can serve as a relatively easy introduction to intersection homology, showing its relations to other homology theories and presenting various applications. Not many prerequisites are required. </p>
<p>In the introduction the reader will find information about the homology and cohomology of manifolds and is instructed that these nice results (e.g. PoincarĂ© duality) are no more valid if we admit manifolds with singularities. It is explained from the very beginning that if we want to extend the relevant results to manifolds with singularities then we must use intersection homology. The next two chapters still have an introductory character. We find here more details about classical simplicial and singular homology and cohomology, the theory of sheaves and sheaf cohomology, and the theory of derived categories. The fourth chapter brings a relatively elementary definition of intersection homology. Many of its basic properties are studied here. The next chapter is then devoted to the application of intersection homology to special topological pseudomanifolds called Witt spaces. Then there is a chapter on the relation between intersection cohomology and L2cohomology, and a chapter on sheaftheoretic intersection homology (this interpretation allows one to prove the topological invariance of intersection homology). </p>
<p>After a chapter devoted to perverse sheaves, there is a chapter where intersection cohomology is applied to toric varieties associated with fans. Chapter 10 is devoted to the Weil conjectures and is oriented towards the Weil conjectures for singular varieties. The next chapter introduces Dmodules and the RiemannHilbert correspondence. Having this material available, the authors then pass on, in the last chapter, to the KazhdanLusztig conjecture. The authors declare that their aim was not to write a fundamental treatise on intersection homology but rather to give propaganda for this new homology. Therefore they give, quite systematically after each chapter, recommendations for further reading. The book can be used as a first reading on intersection homology and its applications. The authors present many examples (and exercises) so that the presentation has quite a concrete character.</p>
</div></div></div></div><div class="field fieldnamefieldreviewreviewer fieldtypetext fieldlabelinline clearfix"><div class="fieldlabel">Reviewer: </div><div class="fielditems"><div class="fielditem even">jiva</div></div></div><span class="vocabulary field fieldnamefieldreviewauthor fieldtypetaxonomytermreference fieldlabelinline clearfix"><h2 class="fieldlabel">Author: </h2><ul class="vocabularylist"><li class="vocabularylinks fielditem even"><a href="/author/fkirwan" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">f. kirwan</a></li><li class="vocabularylinks fielditem odd"><a href="/author/jwoolf" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">j. woolf</a></li></ul></span><span class="vocabulary field fieldnamefieldreviewpublisher fieldtypetaxonomytermreference fieldlabelinline clearfix"><h2 class="fieldlabel">Publisher: </h2><ul class="vocabularylist"><li class="vocabularylinks fielditem even"><a href="/publisher/chapmanhallcrcbocaraton" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">chapman & hall/crc, boca raton</a></li></ul></span><div class="field fieldnamefieldreviewpub fieldtypenumberinteger fieldlabelinline clearfix"><div class="fieldlabel">Published: </div><div class="fielditems"><div class="fielditem even">2006</div></div></div><div class="field fieldnamefieldreviewisbn fieldtypetext fieldlabelinline clearfix"><div class="fieldlabel">ISBN: </div><div class="fielditems"><div class="fielditem even">1584881844</div></div></div><div class="field fieldnamefieldreviewprice fieldtypetext fieldlabelinline clearfix"><div class="fieldlabel">Price: </div><div class="fielditems"><div class="fielditem even">USD 69.95</div></div></div><span class="vocabulary field fieldnamefieldreviewmsc fieldtypetaxonomytermreference fieldlabelhidden"><ul class="vocabularylist"><li class="vocabularylinks fielditem even"><a href="/msc/55algebraictopology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">55 Algebraic topology</a></li></ul></span>
Fri, 30 Sep 2011 16:48:23 +0000
Anonymous
39792 at https://euromathsoc.eu

An Introduction to Intersection Homology Theory
https://euromathsoc.eu/review/introductionintersectionhomologytheory
<div class="field fieldnamefieldreviewreview fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem even"><div class="tex2jax"><p>This book is the second edition of the book of the same title but with only one author, namely F. Kirwan. It appeared as volume 187 in the Pitman Research Notes in Mathematical Sciences (Longman Scientific & Technical, Harlow) in 1988. For this second edition the second author was asked to assist and the text has been substantially extended. The original idea of the first author was to explain intersection homology and bring the reader to the proof (or at least a sketch of the proof) of the KazhdanLusztig conjecture. The book in the present form serves as a relatively easy introduction to intersection homology, shows its relations to other homology theories and presents various applications. Very few prerequisites are needed. </p>
<p>In the introduction the reader will find information about the homology and cohomology of manifolds and is instructed that many nice results (e.g. PoincarĂ© duality) are no longer valid if we admit manifolds with singularities. From the very beginning it is stated that if we want to extend relevant results to manifolds with singularities we must use intersection homology. The next two chapters still have an introductory character. We find more details about classical simplicial and singular homology and cohomology, the theory of sheaves and sheaf cohomology and the theory of derived categories. The fourth chapter provides a relatively elementary definition of intersection homology. Many of its basic properties are studied. The next chapter is then devoted to the application of intersection homology to special topological pseudomanifolds called Witt spaces. Then there is a chapter on the relation of intersection cohomology and L2cohomology, and a chapter on sheaftheoretic intersection homology (this interpretation allows us to prove the topological invariance of intersection homology). After a chapter devoted to perverse sheaves, the next chapter deals with applications of intersection cohomology to toric varieties associated with fans. </p>
<p>Chapter 10 is devoted to the Weil conjectures; it is oriented towards the Weil conjectures for singular varieties. The next chapter introduces Dmodules and the RiemannHilbert correspondence. Having this material at hand, the authors progress onto the KazhdanLusztig conjecture in the last chapter. The authors declare that their aim was not to write a fundamental treatise on intersection homology but rather to provide propaganda for this new homology. Therefore they give, quite systematically after each chapter, recommendations for further reading. The book will be very useful as a first reading on intersection homology and its applications. The authors present many examples (and exercises) so that the presentation has a concrete character.</p>
</div></div></div></div><div class="field fieldnamefieldreviewreviewer fieldtypetext fieldlabelinline clearfix"><div class="fieldlabel">Reviewer: </div><div class="fielditems"><div class="fielditem even">jiva</div></div></div><span class="vocabulary field fieldnamefieldreviewauthor fieldtypetaxonomytermreference fieldlabelinline clearfix"><h2 class="fieldlabel">Author: </h2><ul class="vocabularylist"><li class="vocabularylinks fielditem even"><a href="/author/fkirwan" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">f. kirwan</a></li><li class="vocabularylinks fielditem odd"><a href="/author/jwoolf" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">j. woolf</a></li></ul></span><span class="vocabulary field fieldnamefieldreviewpublisher fieldtypetaxonomytermreference fieldlabelinline clearfix"><h2 class="fieldlabel">Publisher: </h2><ul class="vocabularylist"><li class="vocabularylinks fielditem even"><a href="/publisher/chapmanhallcrc" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">chapman & hall/crc</a></li></ul></span><div class="field fieldnamefieldreviewpub fieldtypenumberinteger fieldlabelinline clearfix"><div class="fieldlabel">Published: </div><div class="fielditems"><div class="fielditem even">2006</div></div></div><div class="field fieldnamefieldreviewisbn fieldtypetext fieldlabelinline clearfix"><div class="fieldlabel">ISBN: </div><div class="fielditems"><div class="fielditem even">1584881844</div></div></div><div class="field fieldnamefieldreviewprice fieldtypetext fieldlabelinline clearfix"><div class="fieldlabel">Price: </div><div class="fielditems"><div class="fielditem even">USD 69.95</div></div></div><span class="vocabulary field fieldnamefieldreviewmsc fieldtypetaxonomytermreference fieldlabelhidden"><ul class="vocabularylist"><li class="vocabularylinks fielditem even"><a href="/msc/55algebraictopology" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">55 Algebraic topology</a></li></ul></span>
Wed, 08 Jun 2011 12:04:16 +0000
Anonymous
39407 at https://euromathsoc.eu