Action dimensions of some simple complexes of groups

Abstract

The action dimension of a discrete group $G$ is the minimum dimension of contractible manifold that admits a proper $G$-action. We compute the action dimension of the direct limit of a simple complex of groups for several classes of examples including: 1) Artin groups, 2) graph products of groups, and 3) fundamental groups of aspherical complements of arrangements of affine hyperplanes.

arXiv commentTypos corrected, some minor restructuring of subsections

References in corpus (6)

• Vanishing theorems and conjectures for the, ${\ell }^2$--homology of right-angled Coxeter groups
• The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group
• Combinatorial covers and vanishing of cohomology
• The action dimension of right-angled Artin groups
• Determining the action dimension of an Artin group by using its complex of abelian subgroups
• A lower bound to the action dimension of a group

Cited by in corpus (1)

• Bordifications of hyperplane arrangements and their curve complexes