The action dimension of Artin groups

DOI10.1007/S10711-019-00502-9arXiv1608.08170MaRDI QIDQ6276976

Giang Le

Publication date: 29 August 2016

Abstract: The emph{action dimension} of a discrete group $G$ is the minimum dimension of a contractible manifold, which admits a proper $G$-action. In this paper, we study the action dimension of general Artin groups. The main result is that the action dimension of an Artin group with the nerve $L$ of dimension $n$ for $ne2$ is less than or equal to $(2n+1)$ if the Artin group satisfies the $K(pi,1)$-Conjecture and the top cohomology group of $L$ with $mathbbZ$-coefficients is trivial. For $n=2$, we need one more condition on $L$ to get the same inequality; that is the fundamental group of $L$ is generated by $r$ elements where $r$ is the rank of $H_1(L,mathbbZ)$.

Mathematics Subject Classification ID

Geometric group theory (20F65) Braid groups; Artin groups (20F36) Topological methods in group theory (57M07)

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