{
  "id": "1107.2154",
  "version": "v3",
  "published": "2011-07-11T21:42:10.000Z",
  "updated": "2013-04-29T17:27:17.000Z",
  "title": "A rank inequality for the knot Floer homology of double branched covers",
  "authors": [
    "Kristen Hendricks"
  ],
  "comment": "This is the final version as published by Algebraic & Geometric Topology (and posted here by the author)",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "Given a knot K in S^3, let \\Sigma(K) be the double branched cover of S^3 over K. We show there is a spectral sequence whose E^1 page is (\\hat{HFK}(\\Sigma(K), K) \\otimes V^{n-1}) \\otimes \\mathbb Z_2((q)), for V a \\mathbb Z_2-vector space of dimension two, and whose E^{\\infty} page is isomorphic to (\\hat{HFK}(S^3, K) \\otimes V^{n-1}) \\otimes \\mathbb Z_2((q)), as \\mathbb Z_2((q))-modules. As a consequence, we deduce a rank inequality between the knot Floer homologies \\hat{HFK}(\\Sigma(K), K) and \\hat{HFK}(S^3, K).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-04-29T17:27:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57R58",
      "53D40"
    ],
    "keywords": [
      "knot floer homology",
      "double branched cover",
      "rank inequality",
      "spectral sequence",
      "isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.2154H"
    }
  }
}