{
  "id": "math/0504519",
  "version": "v2",
  "published": "2005-04-25T13:49:48.000Z",
  "updated": "2006-10-24T18:20:43.000Z",
  "title": "A Presentation For The Automorphisms Of The 3-Sphere That Preserve A Genus Two Heegaard Splitting",
  "authors": [
    "Erol Akbas"
  ],
  "comment": "Completely rewritten. 21 pages with 22 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Scharlemann constructed a connected simplicial 2-complex $\\Gamma$ with an action by the group ${\\mathcal H_{2}}$ of isotopy classes of orientation preserving homeomorphisms of $S^3$ that preserve the isotopy class of an unknotted genus 2 handlebody $V$. In this paper we prove that the 2-complex $\\Gamma$ is contractible. Therefore we get a finite presentation of ${\\mathcal H_{2}}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-24T18:20:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heegaard splitting",
      "automorphisms",
      "orientation preserving homeomorphisms",
      "finite presentation",
      "isotopy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4519A"
    }
  }
}