Outer Automorphisms of Hyperbolic Groups and Small Actions on ℝ-Trees

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Abstract

If Γ is a group, denote by Out(Γ) the group of outer automorphisms of Γ. The definitions of the notions used in this introduction are given in the first section. The main theorem of this paper (section 2) is the following:

Theorem.Let Γ be a finitely generated word hyperbolic group. If Out(Γ) is infinite, then there exists an isometric action of Γ on an-tree with almost cyclic edge stabilizers and without any global fixed point.