{
  "id": "2405.09295",
  "version": "v1",
  "published": "2024-05-15T12:36:18.000Z",
  "updated": "2024-05-15T12:36:18.000Z",
  "title": "Cables of the figure-eight knot via real Frøyshov invariants",
  "authors": [
    "Sungkyung Kang",
    "JungHwan Park",
    "Masaki Taniguchi"
  ],
  "comment": "31 pages, 1 figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that the $(2n,1)$-cable of the figure-eight knot is not smoothly slice when $n$ is odd, by using the real Seiberg-Witten Fr{\\o}yshov invariant of Konno-Miyazawa-Taniguchi. For the computation, we develop an $O(2)$-equivariant version of the lattice homotopy type, originally introduced by Dai-Sasahira-Stoffregen. This enables us to compute the real Seiberg-Witten Floer homotopy type for a certain class of knots. Additionally, we present some computations of Miyazawa's real framed Seiberg-Witten invariant for 2-knots.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-15T12:36:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K41"
    ],
    "keywords": [
      "real frøyshov invariants",
      "figure-eight knot",
      "real seiberg-witten floer homotopy type",
      "miyazawas real framed seiberg-witten invariant",
      "lattice homotopy type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}