{
  "id": "1310.7314",
  "version": "v1",
  "published": "2013-10-28T04:39:56.000Z",
  "updated": "2013-10-28T04:39:56.000Z",
  "title": "On Heegaard splittings of knot exteriors with tunnel number degenerations",
  "authors": [
    "Kanji Morimoto"
  ],
  "comment": "13 pages, 12 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $K_1, K_2$ be two knots with $t(K_1)+t(K_2)>2$ and $t(K_1 # K_2)=2$. Then, in the present paper, we will show that any genus three Heegaard splittings of $E(K_1 # K_2)$ is strongly irreducible and that $E(K_1 # K_2)$ has at most four genus three Heegaard splittings up to homeomorphism. Moreover, we will give a complete classification of those four genus three Heegaard splittings and show unknotting tunnel systems of knots $K_1 # K_2$ corresponding to those Heegaard splittings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-28T04:39:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "heegaard splittings",
      "tunnel number degenerations",
      "knot exteriors",
      "complete classification",
      "unknotting tunnel systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.7314M"
    }
  }
}