Amenable covers of right-angled Artin groups

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.

The spectrum of simplicial volume with fixed fundamental group

“…) is trivial; this includes all groups of type FH d whose classifying space admits an amenable open cover of multiplicity at most d [9,14,18]. Good bounds for such amenable multiplicities are, e.g., known for right-angled Artin groups [16]. More generally, one can also consider multiplicities of (uniformly) boundedly acyclic open covers [15,17].…”

Minimal volume entropy of RAAG's

“…This completes the characterization of nonvanishing 𝜔(𝐴 𝐿 ). The method in [9] works in all dimensions as well, so provides an alternative proof of Theorem 1.1.…”