{
  "id": "0907.4378",
  "version": "v1",
  "published": "2009-07-27T15:24:36.000Z",
  "updated": "2009-07-27T15:24:36.000Z",
  "title": "On the naturality of the spectral sequence from Khovanov homology to Heegaard Floer homology",
  "authors": [
    "J. Elisenda Grigsby",
    "Stephan M. Wehrli"
  ],
  "comment": "36 pages, 13 figures",
  "categories": [
    "math.GT",
    "math.QA",
    "math.SG"
  ],
  "abstract": "Ozsvath and Szabo have established an algebraic relationship, in the form of a spectral sequence, between the reduced Khovanov homology of (the mirror of) a link L in S^3 and the Heegaard Floer homology of its double-branched cover. This relationship has since been recast by the authors as a specific instance of a broader connection between Khovanov- and Heegaard Floer-type homology theories, using a version of Heegaard Floer homology for sutured manifolds developed by Juhasz. In the present work we prove the naturality of the spectral sequence under certain elementary TQFT operations, using a generalization of Juhasz's surface decomposition theorem valid for decomposing surfaces geometrically disjoint from an imbedded framed link.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-27T15:24:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57R58",
      "57M12",
      "81R50"
    ],
    "keywords": [
      "heegaard floer homology",
      "spectral sequence",
      "khovanov homology",
      "naturality",
      "juhaszs surface decomposition theorem valid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.4378E"
    }
  }
}