{
  "id": "math/0403029",
  "version": "v1",
  "published": "2004-03-02T15:07:42.000Z",
  "updated": "2004-03-02T15:07:42.000Z",
  "title": "Heegaard diagrams and holomorphic disks",
  "authors": [
    "Peter Ozsvath",
    "Zoltan Szabo"
  ],
  "comment": "41 pages, 10 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "A three-manifold equipped with a Heegaard diagram can be used to set up a Floer homology theory whose differential counts pseudo-holomorphic disks in the $g$-fold symmetric product of the Heegaard surface. This leads to a topological invariant for three-manifolds, Heegaard Floer homology, which is functorial under cobordisms. In this survey article, we sketch this construction and describe some of its topological applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-03-02T15:07:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "53D40",
      "57M27"
    ],
    "keywords": [
      "heegaard diagram",
      "differential counts pseudo-holomorphic disks",
      "fold symmetric product",
      "heegaard floer homology",
      "floer homology theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3029O"
    }
  }
}