Overview
- Gives a deep insight into the subject through an efficient and entirely original approach
- Provides a clear, highly informative historical presentation of group actions, from the starting point of the theory
- Offers an ideal complement to a course on de Rham cohomology
- Contains numerous concrete examples of the derived duality functor
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2288)
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About this book
This book carefully presents a unified treatment of equivariant Poincaré duality in a wide variety of contexts, illuminating an area of mathematics that is often glossed over elsewhere.
The approach used here allows the parallel treatment of both equivariant and nonequivariant cases. It also makes it possible to replace the usual field of coefficients for cohomology, the field of real numbers, with any field of arbitrary characteristic, and hence change (equivariant) de Rham cohomology to the usual singular (equivariant) cohomology .
The book will be of interest to graduate students and researchers wanting to learn about the equivariant extension of tools familiar from non-equivariant differential geometry.
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Keywords
Table of contents (8 chapters)
Reviews
“The book contains a number of exercises with hints for solutions given in another appendix. There is also an index and an invaluable glossary of symbols organized by chapter. The book is quite technical … .” (Jonathan Hodgson, zbMATH 1473.55001, 2021)
Authors and Affiliations
Bibliographic Information
Book Title: Equivariant Poincaré Duality on G-Manifolds
Book Subtitle: Equivariant Gysin Morphism and Equivariant Euler Classes
Authors: Alberto Arabia
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-70440-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Softcover ISBN: 978-3-030-70439-1Published: 13 June 2021
eBook ISBN: 978-3-030-70440-7Published: 12 June 2021
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XV, 376
Number of Illustrations: 270 b/w illustrations, 2 illustrations in colour
Topics: Algebraic Topology, Topology, Category Theory, Homological Algebra, Group Theory and Generalizations, Field Theory and Polynomials