Bredon cohomological dimension for virtually abelian stabilisers for \(\mathrm{CAT}(0)\) groups. (English) Zbl 07421761
Summary: Given a discrete group \(G\), for any integer \(r\geq 0\) 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 \(\mathrm{CAT}(0)\) 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.
MSC:
| 20F65 | Geometric group theory |
| 20F67 | Hyperbolic groups and nonpositively curved groups |
| 20J05 | Homological methods in group theory |
Keywords:
classifying space for a family of subgroups; Bredon cohomological dimension; geometric dimension; \(\mathrm{CAT}(0)\) groupReferences:
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