{
  "id": "0807.4718",
  "version": "v2",
  "published": "2008-07-29T18:28:03.000Z",
  "updated": "2009-01-07T19:09:13.000Z",
  "title": "Incompressible surfaces, hyperbolic volume, Heegaard genus and homology",
  "authors": [
    "Marc Culler",
    "Jason DeBlois",
    "Peter B. Shalen"
  ],
  "comment": "24 pages, some typographical errors have been corrected and a few passages were reworded to improve clarity",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that if M is a complete, finite-volume, hyperbolic 3-manifold having exactly one cusp, and if H_1(M;Z_2) has dimension at least 6, then M has volume greater than 5.06. We also show that if M is a closed, orientable hyperbolic 3-manifold such that H_1(M;Z_2) has dimension at least 4, and if the image of the cup product map in H^2(M;Z_2) has dimension at most 1, then M has volume greater than 3.08. The proofs of these geometric results involve new topological results relating the Heegaard genus of a closed Haken manifold M to the Euler characteristic of the kishkes (i.e guts) of the complement of an incompressible surface in M.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-01-07T19:09:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "heegaard genus",
      "incompressible surface",
      "hyperbolic volume",
      "volume greater",
      "cup product map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.4718C"
    }
  }
}