{
  "id": "1910.01672",
  "version": "v1",
  "published": "2019-10-03T18:23:04.000Z",
  "updated": "2019-10-03T18:23:04.000Z",
  "title": "Genus one cobordisms between torus knots",
  "authors": [
    "Peter Feller",
    "JungHwan Park"
  ],
  "comment": "19 pages, 12 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We determine the pairs of torus knots that have a genus one cobordism between them, with one notable exception. This is done by combining obstructions using $\\nu^+$ from the Heegaard Floer knot complex and explicit cobordisms constructions. As an application, we determine the induced subgraph of the Gordian graph on the set of vertices that are given by torus knots.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-03T18:23:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57N70"
    ],
    "keywords": [
      "torus knots",
      "heegaard floer knot complex",
      "explicit cobordisms constructions",
      "gordian graph",
      "notable exception"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}