Automorphism and outer automorphism groups of Right-angled Artin groups are not relatively hyperbolic

Abstract

We show that the automorphism groups of right-angled Artin groups whose defining graphs have at least 3 vertices are not relatively hyperbolic. We then show that the outer automorphism groups are not relatively hyperbolic, if they are not virtually isomorphic to a right-angled Artin group whose defining graph is either a single vertex or disconnected.