{
  "id": "2003.13572",
  "version": "v1",
  "published": "2020-03-30T15:48:58.000Z",
  "updated": "2020-03-30T15:48:58.000Z",
  "title": "Dominating surface-group representations into $\\mathrm{PSL}_2 (\\mathbb{C})$ in the relative representation variety",
  "authors": [
    "Subhojoy Gupta",
    "Weixu Su"
  ],
  "comment": "15 pages, 3 figures",
  "categories": [
    "math.GT",
    "math.RT"
  ],
  "abstract": "Let $\\rho$ be a representation of the fundamental group of a punctured surface into $\\mathrm{PSL}_2 (\\mathbb{C})$ that is not Fuchsian. We prove that there exists a Fuchsian representation that strictly dominates $\\rho$ in the simple length spectrum, and preserves the boundary lengths, unless $\\rho$ is degenerate and co-axial. This extends a result of Deroin-Tholozan to the case of a surface with punctures. Our proof involves straightening the pleated plane in $\\mathbb{H}^3$ determined by the Fock-Goncharov coordinates of a framed representation, and applying strip-deformations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-30T15:48:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dominating surface-group representations",
      "relative representation variety",
      "simple length spectrum",
      "fock-goncharov coordinates",
      "fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}