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Equivariant Poincaré Duality on G-Manifolds: Equivariant Gysin Morphism and Equivariant Euler Classes: Lecture Notes in Mathematics, cartea 2288

Autor Alberto Arabia
en Limba Engleză Paperback – 13 iun 2021
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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Specificații

ISBN-13: 9783030704391
ISBN-10: 3030704394
Pagini: 376
Ilustrații: XV, 376 p. 272 illus., 2 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.6 kg
Ediția:1st ed. 2021
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Cham, Switzerland

Cuprins

- Introduction. - Nonequivariant Background. - Poincaré Duality Relative to a Base Space. - Equivariant Background. - Equivariant Poincaré Duality. - Equivariant Gysin Morphism and Euler Classes. - Localization. - Changing the Coefficients Field.

Recenzii

“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)

Textul de pe ultima copertă

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.

Caracteristici

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