{
  "id": "math/0609674",
  "version": "v1",
  "published": "2006-09-24T23:48:30.000Z",
  "updated": "2006-09-24T23:48:30.000Z",
  "title": "Thin position for knots in a 3-manifold",
  "authors": [
    "Maggy Tomova"
  ],
  "comment": "14 pages, 2 figures",
  "doi": "10.1112/jlms/jdp009",
  "categories": [
    "math.GT"
  ],
  "abstract": "We extend the notion of thin multiple Heegaard splittings of a link in a 3-manifold to take into consideration not only compressing disks but also cut-disks for the Heegaard surfaces. We prove that if H is a c-strongly compressible bridge surface for a link K contained in a closed orientable irreducible 3-manifold M then one of the following is satisfied: H is stabilized, H is meridionally stabilized, H is perturbed, a component of K is removable, M contains an essential meridional surface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-24T23:48:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57M50"
    ],
    "keywords": [
      "thin position",
      "thin multiple heegaard splittings",
      "essential meridional surface",
      "c-strongly compressible bridge surface",
      "heegaard surfaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9674T"
    }
  }
}