{
  "id": "1210.7055",
  "version": "v2",
  "published": "2012-10-26T05:36:46.000Z",
  "updated": "2015-09-10T18:54:49.000Z",
  "title": "Splicing knot complements and bordered Floer homology",
  "authors": [
    "Matthew Hedden",
    "Adam Simon Levine"
  ],
  "comment": "25 pages. Revised version, to appear in Crelle's Journal. Errors from the original version have been corrected",
  "doi": "10.1515/crelle-2014-0064",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We show that the integer homology sphere obtained by splicing two nontrivial knot complements in integer homology sphere L-spaces has Heegaard Floer homology rank strictly greater than one. In particular, splicing the complements of nontrivial knots in the 3-sphere never produces an L-space. The proof uses bordered Floer homology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-26T05:36:46.000Z",
      "comment": "23 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-10T18:54:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57R58"
    ],
    "keywords": [
      "bordered floer homology",
      "splicing knot complements",
      "floer homology rank strictly greater",
      "heegaard floer homology rank",
      "nontrivial knot"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7055H"
    }
  }
}