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Lecture Notes in Mathematics

Equivariant Ordinary Homology and Cohomology

Authors: Costenoble, Steven R., Waner, Stefan

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  • * A long-awaited detailed account of an ordinary equivariant (co)homology theory for compact Lie Group actions that is fully stable and has Poincaré Duality for all G-manifolds
  •  * Extends all the commonly used ordinary equivariant theories, including Borel (co)homology, Bredon-Illman (co)homology, and RO(G)-graded ordinary (co)homology
  • * Includes numerous motivating examples and calculations
  • * Includes guides to reading on several levels, from a first reading avoiding technicalities to more in-depth readings 
  • * The first published results on the theory for actions by general compact Lie groups
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About this book

Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries. The discussion is motivated by reference to a list of instructive “toy” examples and calculations in what is a relatively unexplored field. The authors also provide a reading path for the first-time reader less interested in working through sophisticated machinery but still desiring a rigorous understanding of the main concepts. The subject’s classical counterparts, ordinary homology and cohomology, dating back to the work of Henri Poincaré in topology, are calculational and theoretical tools which are important in many parts of mathematics and theoretical physics, particularly in the study of manifolds. Similarly powerful tools have been lacking, however, in the context of equivariant topology. Aimed at advanced graduate students and researchers in algebraic topology and related fields, the book assumes knowledge of basic algebraic topology and group actions.

 

Reviews

“By reading this book the reader will certainly be able to gain a comprehensive grasp of all the key concepts and knowledge required for understanding equivariant homology and cohomology theories for compact Lie groups and thereby hopefully be able to consider respective new perspectives on this subject. This book consists of an introduction and three chapters with bibliography and indexes of notations and subjects.” (Haruo Minami, zbMATH 1362.55001, 2017)


Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-50448-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-319-50447-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Equivariant Ordinary Homology and Cohomology
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2178
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-50448-3
DOI
10.1007/978-3-319-50448-3
Softcover ISBN
978-3-319-50447-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 294
Number of Illustrations
1 b/w illustrations
Topics

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