Amenable covers of right‐angled Artin groups

Abstract

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