{
  "id": "2212.12951",
  "version": "v1",
  "published": "2022-12-25T19:52:56.000Z",
  "updated": "2022-12-25T19:52:56.000Z",
  "title": "A note on rationally slice knots",
  "authors": [
    "Adam Simon Levine"
  ],
  "comment": "9 pages, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Kawauchi proved that every strongly negative amphichiral knot $K \\subset S^3$ bounds a smoothly embedded disk in some rational homology ball $V_K$, whose construction a priori depends on $K$. We show that $V_K$ is independent of $K$ up to diffeomorphism. Thus, a single 4-manifold, along with connected sums thereof, accounts for all known examples of knots that are rationally slice but not slice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-25T19:52:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K18"
    ],
    "keywords": [
      "rationally slice knots",
      "rational homology ball",
      "strongly negative amphichiral knot",
      "connected sums thereof",
      "smoothly embedded disk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}