Arboreal Group Theory

Volume 19 of the series Mathematical Sciences Research Institute Publications pp 331-343

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

  • Frédéric PaulinAffiliated withLaboratoire de Mathématiques, Ecole Normale Supérieure de Lyon

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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.