{
  "id": "2108.04493",
  "version": "v1",
  "published": "2021-08-10T07:55:15.000Z",
  "updated": "2021-08-10T07:55:15.000Z",
  "title": "An obstruction of Gordian distance one and cosmetic crossings for genus one knots",
  "authors": [
    "Tetsuya Ito"
  ],
  "comment": "5 pages, no Figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give an obstruction for genus one knots $K$, $K'$ to have the Gordian distance one by using the $0$th coefficient of the HOMFLT polynomials. As an application, we give a new constraint for genus one knot to admit a (generalized) cosmetic crossing. Combining known results, we prove the (generalized) cosmetic crossing conjecture for genus one pretzel knots.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-10T07:55:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10"
    ],
    "keywords": [
      "gordian distance",
      "obstruction",
      "cosmetic crossing conjecture",
      "homflt polynomials",
      "th coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}