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

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

2005-03-17

arxiv.org/abs/math/0503369v1

Mathematics

Algebraic Geometry

20 pages; an expository paper delivered at the 2004 AMS conference for young algebraic geometers

Scientific paper

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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