Hyperbolic aspects of right-angled Artin groups

Abstract

For each right-angled Artin group G, we canonically associate a quasi-tree T. In the case when G has cohomological dimension two, this graph T precisely encodes all the isomorphism types of right-angled Artin groups that are embedded in G. In general, T provides a necessary condition for such isomorphism types. T turns out to be quasi-isometric to the coned-off Cayley graph of G relative to the centralizers of the vertices. We describe hyperbolic aspects of the action of G on this quasi-tree.