{
  "id": "1404.4803",
  "version": "v1",
  "published": "2014-04-18T14:55:07.000Z",
  "updated": "2014-04-18T14:55:07.000Z",
  "title": "Convex cocompactness and stability in mapping class groups",
  "authors": [
    "Matthew Gentry Durham",
    "Samuel J. Taylor"
  ],
  "comment": "15 pages, 1 figure",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We introduce a strong notion of quasiconvexity in finitely generated groups, which we call stability. Stability agrees with quasiconvexity in hyperbolic groups and is preserved under quasi-isometry for finitely generated groups. We show that the stable subgroups of mapping class groups are precisely the convex cocompact subgroups. This generalizes a well-known result of Behrstock and is related to questions asked by Farb-Mosher and Farb.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-18T14:55:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mapping class groups",
      "convex cocompactness",
      "finitely generated groups",
      "convex cocompact subgroups",
      "stability agrees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.4803G"
    }
  }
}