2005/03/17 by Julianna S. Tymoczko, Julianna Tymoczko, Tymoczko, Julianna S. · 2 citations
Mathematics · #14F43 #55N51 #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #msc:14F43 #msc:55N51
paper · pdf · doi:10.48550/arxiv.math/0503369
20 pages; an expository paper delivered at the 2004 AMS conference for young algebraic geometers
arxiv created 2005/03/17 · openalex publication_date 2005/03/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.