On hyperbolicity and virtual freeness of automorphism groups

Abstract

We show that word hyperbolicity of automorphism groups of graph products $G_{\Gamma }$ and of Coxeter groups $W_{\Gamma }$ depends strongly on the shape of the defining graph $\Gamma$. We also characterized those $Aut(G_{\Gamma })$ and $Aut(W_{\Gamma })$ in terms of $\Gamma$ that are virtually free.

9 pages