{
  "id": "math/0604115",
  "version": "v2",
  "published": "2006-04-05T18:27:44.000Z",
  "updated": "2007-04-29T13:01:37.000Z",
  "title": "Stabilizing Heegaard splittings of toroidal 3-manifolds",
  "authors": [
    "Ryan Derby-Talbot"
  ],
  "comment": "21 pages, 18 figures. Version for publication. Generalization of the main theorem and minor changes in style and format",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $T$ be a separating incompressible torus in a 3-manifold $M$. Assuming that a genus $g$ Heegaard splitting $V \\cup_S W$ can be positioned nicely with respect to $T$ (e.g. $V \\cup_S W$ is strongly irreducible), we obtain an upper bound on the number of stabilizations required for $V \\cup_S W$ to become isotopic to a Heegaard splitting which is an amalgamation along $T$. In particular, if $T$ is a canonical torus in the JSJ decomposition of $M$, then the number of necessary stabilizations is at most $4g-4$. As a corollary, this establishes an upper bound on the number of stabilizations required for $V \\cup_S W$ and any Heegaard splitting obtained by a Dehn twist of $V \\cup_S W$ along $T$ to become isotopic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-04-29T13:01:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99"
    ],
    "keywords": [
      "stabilizing heegaard splittings",
      "upper bound",
      "dehn twist",
      "necessary stabilizations",
      "jsj decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4115D"
    }
  }
}