{
  "id": "2304.10345",
  "version": "v1",
  "published": "2023-04-20T14:34:06.000Z",
  "updated": "2023-04-20T14:34:06.000Z",
  "title": "The ${\\rm SL}(2,\\mathbb{C})$-character variety of an arborescent knot",
  "authors": [
    "Haimiao Chen"
  ],
  "comment": "14 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We clarify steps for determining the ${\\rm SL}(2,\\mathbb{C})$-character variety of any arborescent knot. Interestingly, we show that the `excellent parts' of arborescent knots $K_1,K_2$ are isomorphic if $K_1$ can be related to $K_2$ through certain moves on projection diagrams. Furthermore, we give a sufficient condition in terms of diagram for the existence of components of dimension larger than $1$. A generalization to arborescent links is sketched.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-20T14:34:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K31"
    ],
    "keywords": [
      "arborescent knot",
      "character variety",
      "arborescent links",
      "dimension larger",
      "excellent parts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}