{
  "id": "math/0409498",
  "version": "v1",
  "published": "2004-09-26T04:25:18.000Z",
  "updated": "2004-09-26T04:25:18.000Z",
  "title": "Heegaard Splittings of Boundary Reducible 3-Manifolds",
  "authors": [
    "Jiming Ma",
    "Ruifeng Qiu"
  ],
  "comment": "12 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we shall prove that any Heegaard splitting of a $\\partial$-reducible 3-manifold $M$, say $M=W\\cup V$, can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard splittings of $n$ manifolds $M_{1},..., M_{n}$ where $M_{i}$ is either a solid torus or a $\\partial$-irreducible manifold. Furthermore, $W\\cup V$ is stabilized if and only if one of the factors is stabilized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-26T04:25:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heegaard splitting",
      "boundary reducible",
      "self-boundary connected sums",
      "solid torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9498M"
    }
  }
}