{
  "id": "0807.1432",
  "version": "v3",
  "published": "2008-07-09T12:14:56.000Z",
  "updated": "2008-10-13T13:32:41.000Z",
  "title": "On the Colored Jones Polynomial, Sutured Floer homology, and Knot Floer homology",
  "authors": [
    "J. Elisenda Grigsby",
    "Stephan Wehrli"
  ],
  "comment": "46 pages, 13 figures; Unnecessary assumptions in statement of link surgeries spectral sequence (Section 4) removed, references updated, minor typos corrected throughout",
  "categories": [
    "math.GT",
    "math.QA",
    "math.SG"
  ],
  "abstract": "Let K in S^3 be a knot, and let \\widetilde{K} denote the preimage of K inside its double branched cover, \\Sigma(K). We prove, for each integer n > 1, the existence of a spectral sequence from Khovanov's categorification of the reduced n-colored Jones polynomial of the mirror of K to the knot Floer homology of (\\Sigma(K),\\widetilde{K}) (when n odd) and to (S^3, K # K) (when n even). A corollary of our result is that Khovanov's categorification of the reduced n-colored Jones polynomial detects the unknot whenever n>1.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-10-13T13:32:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57R58",
      "57M12",
      "81R50"
    ],
    "keywords": [
      "knot floer homology",
      "sutured floer homology",
      "khovanovs categorification",
      "reduced n-colored jones polynomial detects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.1432E"
    }
  }
}