{
  "id": "1610.04414",
  "version": "v1",
  "published": "2016-10-14T11:49:10.000Z",
  "updated": "2016-10-14T11:49:10.000Z",
  "title": "On high-dimensional representations of knot groups",
  "authors": [
    "Stefan Friedl",
    "Michael Heusener"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GT",
    "math.RT"
  ],
  "abstract": "Given a hyperbolic knot $K$ and any $n\\geq 2$ the abelian representations and the holonomy representation each give rise to an $(n-1)$-dimensional component in the $\\operatorname{SL}(n,\\Bbb{C})$-character variety. A component of the $\\operatorname{SL}(n,\\Bbb{C})$-character variety of dimension $\\geq n$ is called high-dimensional. It was proved by Cooper and Long that there exist hyperbolic knots with high-dimensional components in the $\\operatorname{SL}(2,\\Bbb{C})$-character variety. We show that given any non-trivial knot $K$ and sufficiently large $n$ the $\\operatorname{SL}(n,\\Bbb{C})$-character variety of $K$ admits high-dimensional components.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-14T11:49:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "knot groups",
      "character variety",
      "high-dimensional representations",
      "hyperbolic knot",
      "admits high-dimensional components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}