Bredon cohomological dimension for virtually abelian stabilisers for CAT(0) 
groups

Prytuła, Tomasz

doi:10.1142/S1793525320500284

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Bredon cohomological dimension for virtually abelian stabilisers for CAT(0) groups

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Prytuła, Tomasz
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1142/S1793525320500284
(Publisher version)

https://doi.org/10.48550/arXiv.1810.08924
(Preprint)

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Citation

Prytuła, T. (2021). Bredon cohomological dimension for virtually abelian stabilisers for CAT(0) groups. Journal of Topology and Analysis, 13(3), 739-751. doi:10.1142/S1793525320500284.

Cite as: https://hdl.handle.net/21.11116/0000-0006-9E45-B

Abstract

Given a discrete group $G$, for any integer $r\geqslant0$ 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 J.-F. Lafont.