{
  "id": "1905.00828",
  "version": "v1",
  "published": "2019-05-02T16:02:39.000Z",
  "updated": "2019-05-02T16:02:39.000Z",
  "title": "Instantons, Bar-Natan homology, and some concordance invariants of knots",
  "authors": [
    "P. B. Kronheimer",
    "T. S. Mrowka"
  ],
  "comment": "97 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "A spectral sequence is established, from Bar-Natan's variant of Khovanov homology to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence from a characteristic-2 version of $F_5$ homology, in Khovanov'sclassification. Concordance invariants of knots are derived from the corresponding instanton homology groups, including a 1-parameter family of homomorphisms $f_r$ from the concordance group to the reals, having the potential to provide independent bounds on the genus and number of double points for immersed surfaces with boundary a given knot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-02T16:02:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "05C15"
    ],
    "keywords": [
      "concordance invariants",
      "bar-natan homology",
      "spectral sequence arises",
      "corresponding instanton homology groups",
      "independent bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 97,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}