Dimension invariants for groups admitting a cocompact model for proper actions
Dimension invariants for groups admitting a cocompact model for proper actions
复制标题
接受协紧模型以进行正确操作的群体的维度不变量
DOI：
10.1515/crelle-2014-0061
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
C. Martínez‐Perez
中科院分区：
文献类型：
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作者：
D. Degrijse;C. Martínez‐Perez
设G是一个群，其真作用X有一个余紧分类空间.我们推导出一个公式的Bredon上同调维数的适当行动的$G $的相对上同调与紧支持的某些对子复形的$X $。我们用这个公式计算了有限群的非正曲单复形的基本群的真作用的Bredon上同调维数。作为一个应用，我们表明，如果一个虚拟的挠自由群的行为正确和室传递的建筑物，其虚拟上同调维数与其Bredon上同调维数相一致。这涵盖了Coxeter群和有限群的图形产品的情况。
Let $G$ be a group that admits a cocompact classifying space for proper actions $X$. We derive a formula for the Bredon cohomological dimension for proper actions of $G$ in terms of the relative cohomology with compact support of certain pairs of subcomplexes of $X$. We use this formula to compute the Bredon cohomological dimension for proper actions of fundamental groups of non-positively curved simple complexes of finite groups. As an application we show that if a virtually torsion-free group acts properly and chamber transitively on a building, its virtual cohomological dimension coincides with its Bredon cohomological dimension. This covers the case of Coxeter groups and graph products of finite groups.