{
  "id": "2104.13065",
  "version": "v1",
  "published": "2021-04-27T09:26:02.000Z",
  "updated": "2021-04-27T09:26:02.000Z",
  "title": "The knot quandle of the twist-spun trefoil is a central extension of a Schläfli quandle",
  "authors": [
    "Ayumu Inoue"
  ],
  "comment": "This paper stands as a completely revised version of arXiv:1808.06276 (12 pages, 4 figures)",
  "categories": [
    "math.GT"
  ],
  "abstract": "A quandle is an algebraic system which excels at describing limited symmetries of a space. We introduce the concept of Schl\\\"{a}fli quandles which are defined relating to chosen rotational symmetries of regular tessellations. On the other hand, quandles have a good chemistry with knot theory. Associated with a knot we have its knot quandle. We show that the knot quandle of the $m$-twist-spun trefoil is a central extension of the Schl\\\"{a}fli quandle related to the regular tessellation $\\{ 3, m \\}$ in the sense of the Schl\\\"{a}fli symbol if $m \\geq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-27T09:26:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K12",
      "52B15"
    ],
    "keywords": [
      "knot quandle",
      "central extension",
      "twist-spun trefoil",
      "schläfli quandle",
      "regular tessellation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}