{
  "id": "1907.09116",
  "version": "v1",
  "published": "2019-07-22T03:21:37.000Z",
  "updated": "2019-07-22T03:21:37.000Z",
  "title": "The $ν^+$-equivalence classes of genus one knots",
  "authors": [
    "Kouki Sato"
  ],
  "comment": "46 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The $\\nu^+$-equivalence is an equivalence relation on the knot concordance group. This relation can be seen as a certain stable equivalence on knot Floer complexes $CFK^{\\infty}$, and many concordance invariants derived from Heegaard Floer theory are invariant under the relation. In this paper, we show that any genus one knot is $\\nu^+$-equivalent to one of the trefoil, its mirror and the unknot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-22T03:21:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "equivalence classes",
      "knot concordance group",
      "knot floer complexes",
      "heegaard floer theory",
      "equivalence relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}