{
  "id": "math/0501140",
  "version": "v4",
  "published": "2005-01-10T16:56:43.000Z",
  "updated": "2009-03-15T21:32:08.000Z",
  "title": "Alternate Heegaard genus bounds distance",
  "authors": [
    "Martin Scharlemann",
    "Maggy Tomova"
  ],
  "comment": "This is the version published by Geometry & Topology on 4 May 2006 (V4: typesetting correction)",
  "journal": "Geom. Topol. 10 (2006) 593-617",
  "doi": "10.2140/gt.2006.10.593",
  "categories": [
    "math.GT"
  ],
  "abstract": "Suppose M is a compact orientable irreducible 3-manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized copy of P or the Hempel distance of the splitting P is no greater than twice the genus of Q. More generally, if P and Q are bicompressible but weakly incompressible connected closed separating surfaces in M then either a) P and Q can be well-separated or b) P and Q are isotopic or c) the Hempel distance of P is no greater than twice the genus of Q.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-03-15T21:32:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M50"
    ],
    "keywords": [
      "alternate heegaard genus bounds distance",
      "connected closed separating surfaces",
      "hempel distance",
      "incompressible connected closed separating"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1140S"
    }
  }
}