AI 中文总结
研究群的简单复形的上同调性质，通过Bridson - Haefliger构造的\(K -\)等变同伦型获取关于群\(K\)分类空间的信息，得到了上同调的有限性性质。
AI 中文摘要
群的简单复形是从偏序集到群范畴满足特定性质的函子，由Bridson和Haefliger引入以编码偏序集上作用的迷向子群。嵌入群\(K\)的群的单纯复形有相关的\(K -\)偏序集。本文解释如何通过Bridson - Haefliger构造的\(K -\)等变同伦型获取关于\(K\)的分类空间的信息，还得到了上同调的有限性性质。
英文摘要
A simple complex of groups is a functor from a poset to the category of groups satisfying certain properties. They were introduced by Bridson and Haefliger as an abstract way to encode isotropy subgroups of actions on posets. A simplex complex of groups which embeds in a group $K$ has an associated $K$-poset. We will explain how to obtain information about the classifying space of $K$ through the $K$-equivariant homotopy type of the construction of Bridson-Haefliger, and we will also obtain finiteness properties of cohomology.
