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An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson

Julianna S. Tymoczko
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Abstract

This paper provides an introduction to equivariant cohomology and homology using the approach of Goresky, Kottwitz, and MacPherson. When a group G acts suitably on a variety X, the equivariant cohomology of X can be computed using the combinatorial data of a skeleton of G-orbits on X. We give both a geometric definition and the traditional definition of equivariant cohomology. We include a discussion of the moment map and an algorithm for finding a set of generators for the equivariant cohomology of X. Many examples and explicit calculations are provided.

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Julianna S. Tymoczko. 2005-03-17. An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson. https://arxiv.org/abs/math/0503369

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