{
  "id": "math/0212088",
  "version": "v1",
  "published": "2002-12-05T16:37:06.000Z",
  "updated": "2002-12-05T16:37:06.000Z",
  "title": "Automorphisms of hyperbolic groups and graphs of groups",
  "authors": [
    "Gilbert Levitt"
  ],
  "comment": "20 pages. Pre'publication su Laboratoire Emile Picard n.252. See also http://picard.ups-tlse.fr",
  "journal": "Geometriae Dedicata 114 (2005) 49-70",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "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 $\\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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-12-05T16:37:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "direct product",
      "one-ended word hyperbolic group",
      "outer automorphism group",
      "free abelian group",
      "torsion-free hyperbolic group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....12088L"
    }
  }
}