Title

The action dimension of Artin groups

Publication Date

8-1-2020

Document Type

Article

Department

Mathematics and Statistics

Publication Title

Geometriae Dedicata

Volume

207

Issue

1

DOI

10.1007/s10711-019-00502-9

First Page

335

Last Page

354

Abstract

The 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 if an Artin group with the nerve L of dimension n for n≠ 2 satisfies the K(π, 1) -Conjecture and the top cohomology group of L with Z-coefficients is trivial, then the action dimension of the Artin group is less than or equal to (2 n+ 1). 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 H1(L, Z).

Funding Number

1510640

Funding Sponsor

National Science Foundation

Keywords

Action dimension, Artin groups, Hyperplane complement

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