{
  "id": "1406.1264",
  "version": "v1",
  "published": "2014-06-05T04:36:13.000Z",
  "updated": "2014-06-05T04:36:13.000Z",
  "title": "On the connectedness of subcomplexes of a disk complex",
  "authors": [
    "Jung Hoon Lee"
  ],
  "comment": "11 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "For a boundary-reducible $3$-manifold $M$ with $\\partial M$ a genus $g$ surface, we show that if $M$ admits a genus $g+1$ Heegaard surface $S$, then the disk complex of $S$ is simply connected. Also we consider the connectedness of the complex of reducing spheres. We investigate the intersection of two reducing spheres for a genus three Heegaard splitting of $\\mathrm{(torus)} \\times I$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-05T04:36:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "disk complex",
      "connectedness",
      "subcomplexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.1264L"
    }
  }
}