{
  "id": "0806.1188",
  "version": "v4",
  "published": "2008-06-06T15:26:01.000Z",
  "updated": "2020-11-02T21:52:03.000Z",
  "title": "Four-free groups and hyperbolic geometry",
  "authors": [
    "Marc Culler",
    "Peter B. Shalen"
  ],
  "comment": "64 pages, 4 figures. This version corrects an error in the third paragraph of the proof of Lemma 13.3",
  "journal": "J. Topol. 5 (2012), no. 1, 81-136",
  "doi": "10.1112/jtopol/jtr028",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give new information about the geometry of closed, orientable hyperbolic 3-manifolds with 4-free fundamental group. As an application we show that such a manifold has volume greater than 3.44. This is in turn used to show that if M is a closed orientable hyperbolic 3-manifold such that vol M < 3.44, then H_1(M;Z/2Z) has dimension at most 7.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-09-15T19:37:42.000Z",
      "comment": "64 pages, 4 figures. This version has been accepted for publication by the Journal of Topology",
      "journal": null
    },
    {
      "version": "v4",
      "updated": "2020-11-02T21:52:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "hyperbolic geometry",
      "four-free groups",
      "fundamental group",
      "volume greater"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.1188C"
    }
  }
}