{
  "id": "2505.03720",
  "version": "v1",
  "published": "2025-05-06T17:47:16.000Z",
  "updated": "2025-05-06T17:47:16.000Z",
  "title": "Smooth concordance of cables of the figure-eight knot",
  "authors": [
    "Sungkyung Kang",
    "JungHwan Park",
    "Masaki Taniguchi"
  ],
  "comment": "comments welcome!",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that every nontrivial cable of the figure-eight knot has infinite order in the smooth knot concordance group. Our main contribution is a uniform proof that applies to all $(2n,1)$-cables of the figure-eight knot. To this end, we introduce a family of concordance invariants $\\kappa_R^{(k)}$, defined via $2^k$-fold branched covers and real Seiberg--Witten Floer $K$-theory. These invariants generalize the real $K$-theoretic Fr\\o yshov invariant developed by Konno, Miyazawa, and Taniguchi.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-06T17:47:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K41"
    ],
    "keywords": [
      "figure-eight knot",
      "smooth concordance",
      "smooth knot concordance group",
      "real seiberg-witten floer",
      "uniform proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}