{
  "id": "1308.0888",
  "version": "v2",
  "published": "2013-08-05T05:06:30.000Z",
  "updated": "2013-11-01T08:24:21.000Z",
  "title": "Subgroups of mapping class groups related to Heegaard splittings and bridge decompositions",
  "authors": [
    "Ken'ichi Ohshika",
    "Makoto Sakuma"
  ],
  "comment": "19 pages: the second version. The assumption of Theorem 3 has been changed from the bounded geometry to the bounded combinatorics",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $M=H_1\\cup_S H_2$ be a Heegaard splitting of a closed orientable 3-manifold $M$ (or a bridge decomposition of a link exterior). Consider the subgroup $\\mathrm{MCG}^0(H_j)$ of the mapping class group of $H_j$ consisting of mapping classes represented by auto-homeomorphisms of $H_j$ homotopic to the identity, and let $G_j$ be the subgroup of the automorphism group of the curve complex $\\mathcal{CC}(S)$ obtained as the image of $\\mathrm{MCG}^0(H_j)$. Then the group $G=<G_1, G_2>$ generated by $G_1$ and $G_2$ preserve the homotopy class in $M$ of simple loops on $S$. In this paper, we study the structure of the group $G$ and the problem to what extent the converse to this observation holds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-01T08:24:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57M07",
      "30F40",
      "20F34"
    ],
    "keywords": [
      "mapping class groups",
      "bridge decomposition",
      "heegaard splitting",
      "link exterior",
      "automorphism group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.0888O"
    }
  }
}