An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson
An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson
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跟随 Goresky、Kottwitz 和 MacPherson 介绍等变上同调和同调
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发表时间：
2005
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通讯作者：
Julianna Tymoczko
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文献类型：
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作者：
Julianna Tymoczko
本文利用Goresky，Kottwitz和MacPherson的方法介绍了等变上同调和同调。当群G适当地作用在簇X上时，X的等变上同调可以利用X上G-轨道骨架的组合数据来计算。给出了等变上同调的几何定义和传统定义。我们包括一个讨论的时刻地图和算法找到一组发电机的等变上同调的X。文中给出了许多算例和显式计算。
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.