The action dimension of Artin groups
Mathematics and Statistics
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).
National Science Foundation
Action dimension, Artin groups, Hyperplane complement
Giang Le. "The action dimension of Artin groups" Geometriae Dedicata (2020): 335-354. https://doi.org/10.1007/s10711-019-00502-9