{
  "id": "2102.01937",
  "version": "v1",
  "published": "2021-02-03T08:37:49.000Z",
  "updated": "2021-02-03T08:37:49.000Z",
  "title": "The ${\\rm SL}(2,\\mathbb{C})$-character variety of a Montesinos knot",
  "authors": [
    "Haimiao Chen"
  ],
  "comment": "12 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "For each Montesinos knot $K$, we find a simple method to determine the ${\\rm SL}(2,\\mathbb{C})$-character variety, and show that it can be decomposed as $\\mathcal{X}_0(K)\\sqcup\\mathcal{X}_1(K)\\sqcup\\mathcal{X}_2(K)\\sqcup\\mathcal{X}'(K)$, where $\\mathcal{X}_0(K)$ consists of trace-free characters, $\\mathcal{X}_1(K)$ consists of characters of \"connected sums\" of representations of the constituent rational links, $\\mathcal{X}_2(K)$ is a high-genus algebraic curve, and $\\mathcal{X}'(K)$ generically consists of finitely many points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-03T08:37:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K31"
    ],
    "keywords": [
      "montesinos knot",
      "character variety",
      "constituent rational links",
      "high-genus algebraic curve",
      "simple method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}