{
  "id": "2011.03954",
  "version": "v1",
  "published": "2020-11-08T11:04:42.000Z",
  "updated": "2020-11-08T11:04:42.000Z",
  "title": "Dominating CAT(-1) surface group representations by Fuchsian ones",
  "authors": [
    "Florestan Martin-Baillon"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that for every representation $ \\rho : \\pi_{1} (S_{g}) \\to \\text{Isom}(X) $ of the fundamental group of a genus $ g \\ge 2 $ surface to the isometry group of a complete $ \\text{CAT}(-1) $ metric space $ X $ there exists a Fuchsian representation $ j $ and a $ (j, \\rho) $-equivariant map from $ \\mathbb{H}^{2} $ to $ X $ which is $ c $ -Lipschitz for some $ c < 1 $, or $ \\rho $ restricts to a Fuchsian representation. This generalizes results of Gueritaud-Kassel-Wolff, Deroin-Tholozan and Daskalopoulos-Mese-Sanders-Vdovina",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-08T11:04:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51F99"
    ],
    "keywords": [
      "surface group representations",
      "dominating cat",
      "fuchsian representation",
      "isometry group",
      "metric space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}