# Automorphisms of Hyperbolic Groups and Graphs of Groups

@article{Levitt2002AutomorphismsOH, title={Automorphisms of Hyperbolic Groups and Graphs of Groups}, author={G. Levitt}, journal={Geometriae Dedicata}, year={2002}, volume={114}, pages={49-70} }

Using the canonical JSJ splitting, we describe the outer automorphism group Out(G) of a one-ended word hyperbolic group G. In particular, we discuss to what extent Out(G) is virtually a direct product of mapping class groups and a free abelian group, and we determine for which groups Out(G) is infinite. We also show that there are only finitely many conjugacy classes of torsion elements in Out(G), for G any torsion-free hyperbolic group. More generally, let Γ be a finite graph of groups… Expand

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