THE AUTOMORPHISM GROUP OF ACCESSIBLE GROUPS MATHIEU CARETTE

Abstract. In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essen-tially obtained by taking extensions of relative automorphism groups of vertex groups, groups of Dehn twists and groups of automorphisms of free products. We apply this description and obtain a criterion for Out(G) to be finitely pre-sented, as well as a necessary and sufficient condition for Out(G) to be finite. Consequences for hyperbolic groups are discussed. 1