{
  "id": "0812.4650",
  "version": "v1",
  "published": "2008-12-26T07:32:17.000Z",
  "updated": "2008-12-26T07:32:17.000Z",
  "title": "(Disk, Essential surface) pairs of Heegaard splittings that intersect in one point",
  "authors": [
    "Jung Hoon Lee"
  ],
  "comment": "9 pages, 5 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider a Heegaard splitting M=H_1 \\cup_S H_2 of a 3-manifold M having an essential disk D in H_1 and an essential surface F in H_2 with |D \\cap F|=1. (We require that boundary of F is in S when H_2 is a compressionbody with non-empty \"minus\" boundary.) Let F be a genus g surface with n boundary components. From S, we obtain a genus g(S)+2g+n-2 Heegaard splitting M=H'_1 \\cup_S' H'_2 by cutting H_2 along F and attaching F \\times [0,1] to H_1. As an application, by using a theorem due to Casson and Gordon, we give examples of 3-manifolds having two Heegaard splittings of distinct genera where one of the two Heegaard splittings is a strongly irreducible non-minimal genus splitting and it is obtained from the other by the above construction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-26T07:32:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M50"
    ],
    "keywords": [
      "heegaard splitting",
      "essential surface",
      "irreducible non-minimal genus splitting",
      "strongly irreducible non-minimal genus",
      "distinct genera"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.4650L"
    }
  }
}