Given a discrete group G, for any integer r ≥ 0 we consider the family of all virtually abelian subgroups of G of rank at most r. We give an upper bound for the Bredon cohomological dimension of G for this family for a certain class of groups acting on CAT(0) spaces. This covers the case of Coxeter groups, Right-angled Artin groups, fundamental groups of special cube complexes and graph products of finite groups. Our construction partially answers a question of Lafont.

中文翻译：

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CAT(0) 组的虚拟阿贝尔稳定器的 Bredon 上同调维数

给定一个离散组G, 对于任何整数r ≥ 0我们考虑所有几乎阿贝尔子群的族G最多等级r. 我们给出 Bredon 上同调维数的上限G对于这个家庭对于某一类群体的行动猫(0)空格。这涵盖了 Coxeter 群、直角 Artin 群、特殊立方复形的基本群和有限群的图积的情况。我们的构造部分回答了拉丰的一个问题。