{
  "id": "math/0607156",
  "version": "v4",
  "published": "2006-07-06T12:20:11.000Z",
  "updated": "2007-09-15T02:39:08.000Z",
  "title": "Knot Floer homology detects fibred knots",
  "authors": [
    "Yi Ni"
  ],
  "comment": "version 4: incorporates referee's suggestions, to appear in Inventiones Mathematicae",
  "doi": "10.1007/s00222-007-0075-9",
  "categories": [
    "math.GT"
  ],
  "abstract": "Ozsv\\'ath and Szab\\'o conjectured that knot Floer homology detects fibred knots in $S^3$. We will prove this conjecture for null-homologous knots in arbitrary closed 3--manifolds. Namely, if $K$ is a knot in a closed 3--manifold $Y$, $Y-K$ is irreducible, and $\\hat{HFK}(Y,K)$ is monic, then $K$ is fibred. The proof relies on previous works due to Gabai, Ozsv\\'ath--Szab\\'o, Ghiggini and the author. A corollary is that if a knot in $S^3$ admits a lens space surgery, then the knot is fibred.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-09-15T02:39:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "57M27",
      "57R30"
    ],
    "keywords": [
      "floer homology detects fibred knots",
      "knot floer homology detects",
      "lens space surgery",
      "conjecture",
      "proof relies"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2007,
      "month": "Sep",
      "volume": 170,
      "number": 3,
      "pages": 577
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007InMat.170..577N"
    }
  }
}