{
  "id": "1801.06563",
  "version": "v1",
  "published": "2018-01-19T19:38:23.000Z",
  "updated": "2018-01-19T19:38:23.000Z",
  "title": "A note on the knot Floer homology of fibered knots",
  "authors": [
    "John A. Baldwin",
    "David Shea Vela-Vick"
  ],
  "comment": "18 pages, 5 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We prove that the knot Floer homology of a fibered knot is nontrivial in its next-to-top Alexander grading. Immediate applications include new proofs of Krcatovich's result that knots with $L$-space surgeries are prime and Hedden and Watson's result that the rank of knot Floer homology detects the trefoil among knots in the 3--sphere. We also generalize the latter result, proving a similar theorem for nullhomologous knots in any 3--manifold. We note that our method of proof inspired Baldwin and Sivek's recent proof that Khovanov homology detects the trefoils. As part of this work, we also introduce a numerical refinement of the Ozsv\\'ath-Szab\\'o contact invariant. This refinement was the inspiration for Hubbard and Saltz's annular refinement of Plamenevskaya's transverse link invariant in Khovanov homology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-19T19:38:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57R58",
      "57R17"
    ],
    "keywords": [
      "fibered knot",
      "knot floer homology detects",
      "plamenevskayas transverse link invariant",
      "ozsvath-szabo contact invariant",
      "khovanov homology detects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}