等变丛与各向同性表示
Equivariant Bundles and Isotropy Representations
摘要：
我们引入了一个新的结构，各向同性广群，组织分裂$Γ$ -空间的轨道数据。我们证明了分裂$Γ$ -CW复形$X$上的等变主$G$ -丛可以通过其各向同性群胚的表示进行有效的分类.例如，如果商复形$A=Γ\backslash X$是一个图，所有边稳定子都是$Γ$的toral子群，我们得到了一个纯组合分类的丛，其结构群$G$是一个紧连通李群。如果$G$是阿贝尔的，我们的方法给出了Lashof-May-Segal和Goresky-Kottwitz-MacPherson的一些结果的组合和几何描述.
英文摘要：
We introduce a new construction, the isotropy groupoid, to organize the orbit data for split $Γ$-spaces. We show that equivariant principal $G$-bundles over split $Γ$-CW complexes $X$ can be effectively classified by means of representations of their isotropy groupoids. For instance, if the quotient complex $A=Γ\backslash X$ is a graph, with all edge stabilizers toral subgroups of $Γ$, we obtain a purely combinatorial classification of bundles with structural group $G$ a compact connected Lie group. If $G$ is abelian, our approach gives combinatorial and geometric descriptions of some results of Lashof-May-Segal and Goresky-Kottwitz-MacPherson.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
