Automorphisms of hyperbolic groups and graphs of groups
Abstract
Using the canonical JSJ splitting, we describe the outer automorphism group $\Out(G)$ of a oneended 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 torsionfree hyperbolic group. More generally, let $\Gamma $ be a finite graph of groups decomposition of an arbitrary group $G$ such that edge groups $G_e$ are rigid (i.e\. $\Out(G_e)$ is finite). We describe the group of automorphisms of $G$ preserving $\Gamma $, by comparing it to direct products of suitably defined mapping class groups of vertex groups.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2002
 arXiv:
 arXiv:math/0212088
 Bibcode:
 2002math.....12088L
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Geometric Topology
 EPrint:
 20 pages. Pre'publication su Laboratoire Emile Picard n.252. See also http://picard.upstlse.fr