{
  "id": "0709.0376",
  "version": "v2",
  "published": "2007-09-04T09:36:52.000Z",
  "updated": "2008-01-24T10:38:56.000Z",
  "title": "An algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty boundary",
  "authors": [
    "Marc Lackenby"
  ],
  "comment": "23 pages, 14 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We provide an algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty boundary. More generally, we supply an algorithm to determine (up to ambient isotopy) all the Heegaard splittings of any given genus for the manifold. As a consequence, the tunnel number of a hyperbolic link is algorithmically computable. Our techniques rely on Rubinstein's work on almost normal surfaces, and also a new structure called a partially flat angled ideal triangulation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-01-24T10:38:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M25"
    ],
    "keywords": [
      "heegaard genus",
      "non-empty boundary",
      "partially flat angled ideal triangulation",
      "heegaard splittings",
      "tunnel number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.0376L"
    }
  }
}