{
  "id": "1009.5018",
  "version": "v3",
  "published": "2010-09-25T15:36:21.000Z",
  "updated": "2012-05-25T17:39:32.000Z",
  "title": "Lipschitz retraction and distortion for subgroups of Out(F_n)",
  "authors": [
    "Michael Handel",
    "Lee Mosher"
  ],
  "comment": "Version 3: 35 pages. Revised for publication. Changes from previous versions: significant economies in exposition. Added an explicit description of the stabilizer of a free splitting, in Lemma 18",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Given a free factor A of the rank n free group F_n, we characterize when the subgroup of Out(F_n) that stabilizes the conjugacy class of A is distorted in Out(F_n). We also prove that the image of the natural embedding of Aut(F_{n-1}) in Aut(F_n) is nondistorted, that the stabilizer in Out(F_n) of the conjugacy class of any free splitting of F_n is nondistorted, and we characterize when the stabilizer of the conjugacy class of an arbitrary free factor system of F_n is distorted. In all proofs of nondistortion, we prove the stronger statement that the subgroup in question is a Lipschitz retract. As applications we determine Dehn functions and automaticity for Out(F_n) and Aut(F_n).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-05-25T17:39:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "57M07"
    ],
    "keywords": [
      "lipschitz retraction",
      "conjugacy class",
      "distortion",
      "arbitrary free factor system",
      "determine dehn functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.5018H"
    }
  }
}