{
  "id": "0902.0576",
  "version": "v1",
  "published": "2009-02-03T18:33:32.000Z",
  "updated": "2009-02-03T18:33:32.000Z",
  "title": "Volume and topology of bounded and closed hyperbolic 3-manifolds",
  "authors": [
    "Jason DeBlois",
    "Peter B. Shalen"
  ],
  "comment": "38 pages, 1 figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let N be a compact, orientable hyperbolic 3-manifold with connected, totally geodesic boundary of genus 2. If N has Heegaard genus at least 5, then its volume is greater than 6.89. The proof of this result uses the following dichotomy: either N has a long return path (defined by Kojima-Miyamoto), or N has an embedded, codimension-0 submanifold X with incompressible boundary $T \\sqcup \\partial N$, where T is the frontier of X in N, which is not a book of I-bundles. As an application of this result, we show that if M is a closed, orientable hyperbolic 3-manifold such that H_1(M;Z_2) has dimension at least 5, and if the image in H^2(M;Z_2) of the cup product map has image of dimension at most 1, then M has volume greater than 3.44.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-03T18:33:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "closed hyperbolic",
      "orientable hyperbolic",
      "cup product map",
      "long return path",
      "volume greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.0576D"
    }
  }
}