Groups quasi-isometric to RAAG's

TL;DR

This paper characterizes groups that are quasi-isometric to certain right-angled Artin groups with finite outer automorphism groups, showing they admit specific geometric actions on $CAT(0)$ cube complexes related to Davis buildings.

Contribution

It provides a geometric characterization of groups quasi-isometric to RAAGs with finite outer automorphism groups, linking them to actions on $CAT(0)$ cube complexes with fibering over Davis buildings.

Findings

Groups quasi-isometric to these RAAGs admit geometric actions on $CAT(0)$ cube complexes.

Such complexes have an equivariant fibering over the Davis building.

The characterization applies specifically to RAAGs with finite outer automorphism groups.

Abstract

We characterize groups quasi-isometric to a right-angled Artin group $G$ with finite outer automorphism group. In particular all such groups admit a geometric action on a $CAT(0)$ cube complex that has an equivariant "fibering" over the Davis building of $G$.