Equivariant Ordinary Homology and Cohomology

Authors: Steven R. Costenoble, Stefan Waner



* 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

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.

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