Automorphisms of higher-dimensional right-angled Artin groups

TL;DR

This paper investigates the automorphism groups of higher-dimensional right-angled Artin groups, establishing their virtual torsion-freeness and finite virtual cohomological dimension, thus extending previous two-dimensional results.

Contribution

It generalizes known properties of automorphism groups from two-dimensional to higher-dimensional right-angled Artin groups.

Findings

Automorphism groups are virtually torsion-free.

They have finite virtual cohomological dimension.

Extension of previous two-dimensional results.

Abstract

We study the algebraic structure of the automorphism group of a general right-angled Artin group. We show that this group is virtually torsion-free and has finite virtual cohomological dimension. This generalizes results proved by the authors and John Crisp (arXiv:math/0610980) for two-dimensional right-angled Artin groups.