On the acylindrical hyperbolicity of automorphism groups of right-angled Artin groups

Anthony Genevois

Published 2018-07-02Version 1

In this article, we are interested in the following question: when is the automorphism group of a right-angled Artin group acylindrically hyperbolic? We propose a conjecture, and verify it for molecular graphs, ie., finite simplicial graphs which are connected, triangle-free, square-free and leafless. More precisely, we show that, if $\Gamma$ is a molecular graph which does not decompose as a star, then the automorphism group $\mathrm{Aut}(A_\Gamma)$ is acylindrically hyperbolic.