Sur les automorphismes extérieurs des groupes hyperboliques

Abstract

We prove that an infinite nilpotent group of outer automorphisms in any word-hyperbolic group fixes projectively an action on an R -tree. In particular, we give short proofs of the theorem that any outer automorphism of a free group has a fixed point in the compactified Culler-Vogtmann Outer Space, and of Scott's conjecture on the rank of the fixed points subgroup of a free group automorphism.