{
  "id": "1009.2279",
  "version": "v1",
  "published": "2010-09-13T01:18:09.000Z",
  "updated": "2010-09-13T01:18:09.000Z",
  "title": "Genus two Heegaard splittings of exteriors of 1-genus 1-bridge knots II",
  "authors": [
    "Hiroshi Goda",
    "Chuichiro Hayashi"
  ],
  "comment": "21 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "A knot K is called a 1-genus 1-bridge knot in a 3-manifold M if (M,K) has a Heegaard splitting (V_1,t_1)\\cup (V_2,t_2) where V_i is a solid torus and t_i is a boundary parallel arc properly embedded in V_i. If the exterior of a knot has a genus 2 Heegaard splitting, we say that the knot has an unknotting tunnel. Naturally the exterior of a 1-genus 1-bridge knot K allows a genus 2 Heegaard splitting, i.e., K has an unknotting tunnel. But, in general, there are unknotting tunnels which are not derived form this procedure. Some of them may be levelled with the torus \\partial V_1=\\partial V_2, whose case was studied in our previous paper. In this paper, we consider the remaining case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-13T01:18:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "heegaard splitting",
      "unknotting tunnel",
      "boundary parallel arc",
      "solid torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.2279G"
    }
  }
}