Amenable covers of right-angled Artin groups

2022/04/03 by Kevin Li, Li, Kevin · 1 citation
Mathematics · #20F36 #55M30 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2204.01162

openalex publication_date 2022/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A_L be the right-angled Artin group associated to a finite flag complex L. We show that the amenable category of A_L equals the virtual cohomological dimension of the right-angled Coxeter group W_L. In particular, right-angled Artin groups satisfy a question of Capovilla--Löh--Moraschini proposing an inequality between the amenable category and Farber's topological complexity.

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