Bredon cohomological dimensions for groups acting on CAT(0)-spaces
Bredon cohomological dimensions for groups acting on CAT(0)-spaces
复制标题
作用于 CAT(0) 空间的群的 Bredon 上同调维数
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
N. Petrosyan
中科院分区：
文献类型：
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作者：
D. Degrijse;N. Petrosyan
设G是拓扑维数有界的可分完备CAT（0）-空间上具有离散轨道的等距作用群。在一定条件下，给出了有限子群族和虚循环子群族G的Bredon上同调维数的上界.作为应用，我们证明了亏格g大于1的任意闭连通可定向曲面的映射类群都存在一个具有虚循环稳定子的（9 g-8）维分类空间.此外，我们的结果适用于基本组的图形的群体和群体的欧几里德建筑物。特别是，我们证明了所有的正特征的线性群有一个有限维的分类空间的正常行动和一个有限维的分类空间的家庭的虚拟循环子群。我们还表明，每个广义Baumslag-Solitar群有一个3维模型的分类空间与虚拟循环稳定。
Let G be a group acting isometrically with discrete orbits on a separable complete CAT(0)-space of bounded topological dimension. Under certain conditions, we give upper bounds for the Bredon cohomological dimension of G for the families of finite and virtually cyclic subgroups. As an application, we prove that the mapping class group of any closed, connected, and orientable surface of genus g greater than 1 admits a (9g-8)-dimensional classifying space with virtually cyclic stabilizers. In addition, our results apply to fundamental groups of graphs of groups and groups acting on Euclidean buildings. In particular, we show that all finitely generated linear groups of positive characteristic have a finite dimensional classifying space for proper actions and a finite dimensional classifying space for the family of virtually cyclic subgroups. We also show that every generalized Baumslag-Solitar group has a 3-dimensional model for the classifying space with virtually cyclic stabilizers.