{
  "id": "2011.12287",
  "version": "v1",
  "published": "2020-11-24T18:57:29.000Z",
  "updated": "2020-11-24T18:57:29.000Z",
  "title": "The cobordism distance between a knot and its reverse",
  "authors": [
    "Charles Livingston"
  ],
  "comment": "6 pages, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The cobordism distance between knots, d(K,J), equals the four-genus g_4(K # -J). We consider d(K,K^r), where K^r is the reverse of K. It is elementary that 0 \\le d(K,K^r) \\le 2g_4(K) and it is known that there are knots K for which d(K,K^r) is arbitrarily large. Here it is shown that for any knot for which g_4(K) = g_3(K) (such as non-slice knots with g_3(K) = 1 or strongly quasi-positive knots), one has that d(K,K^r) is strictly less that twice g_4(K). It is shown that for arbitrary positive g, there exist knots for which d(K,K^r) = g = g_4(K). There are no known examples for which d(K,K^r) > g_4(K).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-24T18:57:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10"
    ],
    "keywords": [
      "cobordism distance",
      "non-slice knots",
      "four-genus",
      "elementary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}