{
  "id": "1901.02488",
  "version": "v1",
  "published": "2019-01-08T19:51:44.000Z",
  "updated": "2019-01-08T19:51:44.000Z",
  "title": "A surgery formula for knot Floer homology",
  "authors": [
    "Matthew Hedden",
    "Adam Simon Levine"
  ],
  "comment": "86 pages, 6 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "Let $K$ be a rationally null-homologous knot in a $3$-manifold $Y$, equipped with a nonzero framing $\\lambda$, and let $Y_\\lambda(K)$ denote the result of $\\lambda$-framed surgery on $Y$. Ozsv\\'ath and Szab\\'o gave a formula for the Heegaard Floer homology groups of $Y_\\lambda(K)$ in terms of the knot Floer complex of $(Y,K)$. We strengthen this formula by adding a second filtration that computes the knot Floer complex of the dual knot $K_\\lambda$ in $Y_\\lambda$, i.e., the core circle of the surgery solid torus. In the course of proving our refinement we derive a combinatorial formula for the Alexander grading which may be of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-08T19:51:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25",
      "57R58"
    ],
    "keywords": [
      "knot floer homology",
      "surgery formula",
      "knot floer complex",
      "heegaard floer homology groups",
      "surgery solid torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 86,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}