{
  "id": "1011.1317",
  "version": "v4",
  "published": "2010-11-05T03:30:02.000Z",
  "updated": "2017-04-03T23:50:33.000Z",
  "title": "Heegaard Floer homology and integer surgeries on links",
  "authors": [
    "Ciprian Manolescu",
    "Peter Ozsvath"
  ],
  "comment": "231 pages, 54 figures; major revision: we now work with one U variable for each w basepoint, rather than one per link component; we also added Section 4, with an overview of the main result",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let L be a link in an integral homology three-sphere. We give a description of the Heegaard Floer homology of integral surgeries on L in terms of some data associated to L, which we call a complete system of hyperboxes for L. Roughly, a complete systems of hyperboxes consists of chain complexes for (some versions of) the link Floer homology of L and all its sublinks, together with several chain maps between these complexes. Further, we introduce a way of presenting closed four-manifolds with b_2^+ > 1 by four-colored framed links in the three-sphere. Given a link presentation of this kind for a four-manifold X, we then describe the Ozsvath-Szabo mixed invariants of X in terms of a complete system of hyperboxes for the link. Finally, we explain how a grid diagram produces a particular complete system of hyperboxes for the corresponding link.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-18T21:24:51.000Z",
      "comment": "174 pages, 41 figures; expanded Section 8.1 and added Section 8.6; changed the definition of the complex associated to a sublink (in Section 11.1)",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2017-04-03T23:50:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "57R57"
    ],
    "keywords": [
      "heegaard floer homology",
      "integer surgeries",
      "complete system",
      "grid diagram produces",
      "integral homology three-sphere"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 231,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.1317M"
    }
  }
}