{
  "id": "0903.3509",
  "version": "v1",
  "published": "2009-03-20T14:07:39.000Z",
  "updated": "2009-03-20T14:07:39.000Z",
  "title": "Stabilization, amalgamation, and curves of intersection of Heegaard splittings",
  "authors": [
    "Ryan Derby-Talbot"
  ],
  "comment": "Version for publication. To appear in Algebraic and Geometric Topology",
  "categories": [
    "math.GT"
  ],
  "abstract": "We address a special case of the Stabilization Problem for Heegaard splittings, establishing an upper bound on the number of stabilizations required to make a Heegaard splitting of a Haken 3-manifold isotopic to an amalgamation along an essential surface. As a consequence we show that for any positive integer $n$ there are 3-manifolds containing an essential torus and a Heegaard splitting such that the torus and splitting surface must intersect in at least $n$ simple closed curves. These give the first examples of lower bounds on the minimum number of curves of intersection between an essential surface and a Heegaard surface that are greater than one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-20T14:07:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99"
    ],
    "keywords": [
      "heegaard splitting",
      "intersection",
      "amalgamation",
      "essential surface",
      "essential torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.3509D"
    }
  }
}