2016/08/29 by Giang Le, Le, Giang
Mathematics · #20F36 #20F65 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #math.GT #msc:20F36 #msc:20F65
paper · pdf · doi:10.48550/arxiv.1608.08170
Second version, made the text more readable
openalex publication_date 2016/08/29 · arxiv created 2016/09/29 · arxiv updated 2016/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the action dimension of an Artin group with the nerve L of dimension n for n ≠ 2 is less than or equal to (2n + 1) if the Artin group satisfies the K(π, 1)-Conjecture and the top cohomology group of L with ℤ-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 H1(L, ℤ).