{
  "id": "1005.4346",
  "version": "v1",
  "published": "2010-05-24T15:02:32.000Z",
  "updated": "2010-05-24T15:02:32.000Z",
  "title": "Khovanov homology is an unknot-detector",
  "authors": [
    "P. B. Kronheimer",
    "T. S. Mrowka"
  ],
  "comment": "124 pages, 13 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is isomorphic to the instanton Floer homology of the sutured knot complement: an invariant that is already known to detect the unknot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-24T15:02:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "57M25"
    ],
    "keywords": [
      "khovanov homology",
      "reduced khovanov cohomology",
      "unknot-detector",
      "instanton floer homology",
      "singular instantons"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 124,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.4346K"
    }
  }
}