{
  "id": "2410.12344",
  "version": "v1",
  "published": "2024-10-16T08:05:09.000Z",
  "updated": "2024-10-16T08:05:09.000Z",
  "title": "Knots whose braided satellite have the same HOMFLY polynomial up to given $z$-degrees",
  "authors": [
    "Tetsuya Ito"
  ],
  "comment": "5 pages, no figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "For a given knot $K$ and $w>0$, we construct infinitely many mutually distinct hyperbolic knots $\\{K_i\\}$ such that the $P$-satellites of $K$ and $K_i$ have the same HOMFLY polynomial up to given $z$-degrees, for all braided patterns $P$ with winding number less than or equal to $w$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-16T08:05:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homfly polynomial",
      "braided satellite",
      "mutually distinct hyperbolic knots",
      "braided patterns",
      "winding number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}