{
  "id": "1002.3034",
  "version": "v2",
  "published": "2010-02-16T09:00:44.000Z",
  "updated": "2010-05-20T11:12:27.000Z",
  "title": "An estimation of Hempel distance by using Reeb graph",
  "authors": [
    "Ayako Ido"
  ],
  "comment": "17 pages, 22 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $P, Q$ be Heegaard surfaces of a closed orientable 3-manifold. In this paper, we introduce a method for giving an upper bound of Hempel distance of $P$ by using the Reeb graph derived from a certain horizontal arc in the ambient space $[0,1]\\times[0,1]$ of the Rubinstein-Scharlemann graphic derived from $P$ and $Q$. This is a refinement of a part of Johnson's arguments used for determining stable genera required for flipping high distance Heegaard splittings.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-20T11:12:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M50",
      "57M99"
    ],
    "keywords": [
      "reeb graph",
      "hempel distance",
      "flipping high distance heegaard splittings",
      "estimation",
      "horizontal arc"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.3034I"
    }
  }
}