{
  "id": "1904.12014",
  "version": "v1",
  "published": "2019-04-26T18:48:33.000Z",
  "updated": "2019-04-26T18:48:33.000Z",
  "title": "Knot reversal and mutation act non-trivially on the concordance group of topologically slice knots",
  "authors": [
    "Charles Livingston"
  ],
  "comment": "8 pages, 1 figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "We construct a topologically slice knot that is not smoothly concordant to its reverse. Moreover, we show that string reversal induces a nontrivial involution on the quotient of the concordance group of topologically slice knots modulo the subgroup generated by knots of Alexander polynomial one. This implies that Conway mutation acts non-trivially on these concordance groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-26T18:48:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "concordance group",
      "knot reversal",
      "topologically slice knots modulo",
      "conway mutation acts",
      "string reversal induces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}