{
  "id": "0803.2751",
  "version": "v2",
  "published": "2008-03-19T04:14:57.000Z",
  "updated": "2013-08-26T15:17:10.000Z",
  "title": "Hyperbolic volume and Heegaard distance",
  "authors": [
    "Tsuyoshi Kobayashi",
    "Yo'av Rieck"
  ],
  "comment": "12pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove (Theorem~1.5) that there exists a constant $\\Lambda > 0$ so that if $M$ is a $(\\mu,d)$-generic complete hyperbolic 3-manifold of volume $\\vol[M] < \\infty$ and $\\Sigma \\subset M$ is a Heegaard surface of genus $g(\\Sigma) > \\Lambda \\vol[M]$, then $d(\\Sigma) \\leq 2$, where $d(\\Sigma)$ denotes the distance of $\\Sigma$ as defined by Hempel. The key for the proof of the main result is Theorem~1.8 which is on independent interest. There we prove that if $M$ is a compact 3-manifold that can be triangulated using at most $t$ tetrahedra (possibly with missing or truncated vertices), and $\\Sigma$ is a Heegaard surface for $M$ with $g(\\Sigma) \\geq 76t+26$, then $d(\\Sigma) \\leq 2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-26T15:17:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "57M25"
    ],
    "keywords": [
      "heegaard distance",
      "hyperbolic volume",
      "heegaard surface",
      "generic complete hyperbolic",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.2751K"
    }
  }
}