{
  "id": "1110.1297",
  "version": "v2",
  "published": "2011-10-06T15:26:47.000Z",
  "updated": "2018-07-24T11:30:09.000Z",
  "title": "Gauge theory and Rasmussen's invariant",
  "authors": [
    "P. B. Kronheimer",
    "T. S. Mrowka"
  ],
  "comment": "This version bundles the original submission with a 1-page corrigendum, indicating the error. 23 pages, 3 figures",
  "doi": "10.1112/jtopol/jtt008",
  "categories": [
    "math.GT"
  ],
  "abstract": "A previous paper of the authors' contained an error in the proof of a key claim, that Rasmussen's knot-invariant s(K) is equal to its gauge-theory counterpart. The original paper is included here together with a corrigendum, indicating which parts still stand and which do not.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-06T15:26:47.000Z",
      "abstract": "We show that Rasmussen's knot-invariant, which provided a lower bound for the slice-genus of knots in the 3-sphere, is equal to an invariant which can be defined in a very similar manner using instanton knot homology. As a corollary, it is shown that Rasmussen's invariant provides a bound for the genus of a bounding surface not only in the standard 4-ball, but in any homotopy 4-ball. Thus, this knot-invariant cannot be used to detect counterexamples to the smooth 4-dimensional Poincar\\'e conjecture.",
      "comment": "21 pages, 3 figures",
      "journal": null
    },
    {
      "version": "v2",
      "updated": "2018-07-24T11:30:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "57R60"
    ],
    "keywords": [
      "rasmussens invariant",
      "gauge theory",
      "instanton knot homology",
      "poincare conjecture",
      "lower bound"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.1297K"
    }
  }
}