{
  "id": "math/0508208",
  "version": "v4",
  "published": "2005-08-11T17:12:56.000Z",
  "updated": "2009-07-06T14:55:35.000Z",
  "title": "Dehn surgery, homology and hyperbolic volume",
  "authors": [
    "Ian Agol",
    "Marc Culler",
    "Peter B Shalen"
  ],
  "comment": "This is the version published by Algebraic & Geometric Topology on 8 December 2006",
  "journal": "Algebr. Geom. Topol. 6 (2006) 2297-2312",
  "doi": "10.2140/agt.2006.6.2297",
  "categories": [
    "math.GT"
  ],
  "abstract": "If a closed, orientable hyperbolic 3--manifold M has volume at most 1.22 then H_1(M;Z_p) has dimension at most 2 for every prime p not 2 or 7, and H_1(M;Z_2) and H_1(M;Z_7) have dimension at most 3. The proof combines several deep results about hyperbolic 3--manifolds. The strategy is to compare the volume of a tube about a shortest closed geodesic C in M with the volumes of tubes about short closed geodesics in a sequence of hyperbolic manifolds obtained from M by Dehn surgeries on C.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-07-06T14:55:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57M27"
    ],
    "keywords": [
      "dehn surgery",
      "hyperbolic volume",
      "short closed geodesics",
      "deep results",
      "shortest closed geodesic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8208A"
    }
  }
}