{
  "id": "1105.5508",
  "version": "v1",
  "published": "2011-05-27T09:45:28.000Z",
  "updated": "2011-05-27T09:45:28.000Z",
  "title": "Heegaard Floer homologies for (+1) surgeries on torus knots",
  "authors": [
    "Maciej Borodzik",
    "András Némethi"
  ],
  "comment": "12 pages, 1 figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "We compute the Heegaard Floer homology of $S^3_1(K)$ (the (+1) surgery on the torus knot $T_{p,q}$) in terms of the semigroup generated by $p$ and $q$, and we find a compact formula (involving Dedekind sums) for the corresponding Ozsvath--Szabo d-invariant. We relate the result to known knot invariants of $T_{p,q}$ as the genus and the Levine--Tristram signatures. Furthermore, we emphasize the striking resemblance between Heegaard Floer homologies of (+1) and (-1) surgeries on torus knots. This relation is best seen at the level of $\\tau$ functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-27T09:45:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "heegaard floer homology",
      "torus knot",
      "dedekind sums",
      "compact formula",
      "corresponding ozsvath-szabo d-invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.5508B"
    }
  }
}