{
  "id": "2404.09283",
  "version": "v1",
  "published": "2024-04-14T15:26:02.000Z",
  "updated": "2024-04-14T15:26:02.000Z",
  "title": "Pairs of knot invariants",
  "authors": [
    "Kouki Taniyama"
  ],
  "comment": "31 pages, 23 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $\\alpha$ be a map from the set of all knot types ${\\mathcal K}$ to a set $X$. Let $\\beta$ be a map from ${\\mathcal K}$ to a set $Y$. We define the relation between $\\alpha$ and $\\beta$ to be the image of a map $(\\alpha,\\beta)$ from ${\\mathcal K}$ to $X\\times Y$ sending an element $K$ of ${\\mathcal K}$ to $(\\alpha(K),\\beta(K))$. We determine the relations between $\\alpha$ and $\\beta$ for certain $\\alpha$ and $\\beta$ such as crossing number, unknotting number, bridge number, braid index, genus and canonical genus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-14T15:26:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10"
    ],
    "keywords": [
      "knot invariants",
      "knot types",
      "bridge number",
      "braid index",
      "crossing number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}