{
  "id": "0904.1881",
  "version": "v3",
  "published": "2009-04-12T19:27:23.000Z",
  "updated": "2011-04-18T02:53:29.000Z",
  "title": "Stabilizers of $\\mathbb R$-trees with free isometric actions of $F_N$",
  "authors": [
    "Ilya Kapovich",
    "Martin Lustig"
  ],
  "comment": "corrected the proof of Proposition 4.1, plus several minor fixes and updates; to appear in Journal of Group Theory",
  "journal": "J. Group Theory 14 (2011), no. 5, pp. 673-694",
  "doi": "10.1515/jgt.2010.070",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We prove that if $T$ is an $\\mathbb R$-tree with a minimal free isometric action of $F_N$, then the $Out(F_N)$-stabilizer of the projective class $[T]$ is virtually cyclic. For the special case where $T=T_+(\\phi)$ is the forward limit tree of an atoroidal iwip element $\\phi\\in Out(F_N)$ this is a consequence of the results of Bestvina, Feighn and Handel, via very different methods. We also derive a new proof of the Tits alternative for subgroups of $Out(F_N)$ containing an iwip (not necessarily atoroidal): we prove that every such subgroup $G\\le Out(F_N)$ is either virtually cyclic or contains a free subgroup of rank two. The general case of the Tits alternative for subgroups of $Out(F_N)$ is due to Bestvina, Feighn and Handel.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-04-18T02:53:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stabilizer",
      "minimal free isometric action",
      "virtually cyclic",
      "atoroidal iwip element",
      "tits alternative"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1881K"
    }
  }
}