{
  "id": "math/0408199",
  "version": "v4",
  "published": "2004-08-15T00:25:58.000Z",
  "updated": "2007-01-14T22:55:56.000Z",
  "title": "Heegaard surfaces and measured laminations, II: non-Haken 3-manifolds",
  "authors": [
    "Tao Li"
  ],
  "journal": "J. Amer. Math. Soc., 19 (2006) 625-657",
  "categories": [
    "math.GT"
  ],
  "abstract": "A famous example of Casson and Gordon shows that a Haken 3-manifold can have an infinite family of irreducible Heegaard splittings with different genera. In this paper, we prove that a closed non-Haken 3-manifold has only finitely many irreducible Heegaard splittings, up to isotopy. This is much stronger than the Waldhausen conjecture. Another immediate corollary is that for any irreducible non-Haken 3-manifold M, there is a number N, such that any two Heegaard splittings of M are equivalent after at most N stabilizations.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-01-14T22:55:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57N10",
      "57M25"
    ],
    "keywords": [
      "heegaard surfaces",
      "measured laminations",
      "irreducible heegaard splittings",
      "waldhausen conjecture",
      "immediate corollary"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "J. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8199L"
    }
  }
}