The action dimension of Artin groups
Publication Date
8-1-2020
Document Type
Article
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
Department
Mathematics and Statistics
Recommended Citation
Giang Le. "The action dimension of Artin groups" Geometriae Dedicata (2020): 335-354. https://doi.org/10.1007/s10711-019-00502-9
