Analysis and Algebra on Differentiable Manifolds : a workbook for students and teachers

The book "Analysis and Algebra of Dierentiable Manifolds" contains a
collection of solved problems on diverse topics enclosed in the theory of dier-
entiable manifolds and their geometry. Although the text does not cover the
theory to which the problems refer, it includes introductory explanations at the
beginning of each section. In addition, appropriate references containing the
theory needed to solve the problems are pointed out. At the end of each chap-
ter other related references and further readings are suggested. It also contains
66 gures.
The book is organized as follows. The rst three chapters comprehend all
the topics included in an standard course on dierentiable manifolds at an un-
dergraduate level, starting from the very denition of a dierentiable manifold,
passing through its tensor algebra, and ending with integration on manifolds
and de Rham cohomology. This rst part is of great value for both students
and teachers. The second part of the book is devoted to Lie groups, Rieman-
nian geometry and bre bundles, subjects that must be part of a dierential
geometer's background. The problems selected in this second part cover from
an advance undergraduate level to a Master level. The importance of these
chapters is that they treat topics for which signicant examples and problems
are very difficult to nd in the literature. This collection of exercises allows the
reader to explore and to handle many concepts which otherwise could remain
just as theoretical objects.

Ignacio Luján
Universidad Complutense de Madrid
Book details

The book contains a collection of solved problems on several topics of Differentiable Manifolds and their geometry.

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