Equivariant Poincaré Duality on G-Manifolds
Equivariant Gysin Morphism and Equivariant Euler Classes
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Beschreibung
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.
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.
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
Autor*in
Alberto Arabia
Themen in »Equivariant Poincaré Duality on G-Manifolds«
Derived Category Gysin Morphism Linear Representations of Compact Lie Groups Poincaré Duality Sheaf Cohomology
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“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)
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