{
  "id": "2009.05191",
  "version": "v1",
  "published": "2020-09-11T01:22:49.000Z",
  "updated": "2020-09-11T01:22:49.000Z",
  "title": "Convex co-compact representations of 3-manifold groups",
  "authors": [
    "Mitul Islam",
    "Andrew Zimmer"
  ],
  "comment": "40 pages. Comments welcome",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. We prove that the fundamental group of a closed irreducible orientable 3-manifold can admit such a representation only when the manifold is geometric (with Euclidean, Hyperbolic, or Euclidean $\\times$ Hyperbolic geometry) or when every component in the geometric decomposition is hyperbolic. In each case, we describe the structure of such examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-11T01:22:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A20",
      "53A35",
      "20F67",
      "57M50",
      "20H10"
    ],
    "keywords": [
      "convex co-compact representations",
      "projective general linear group",
      "image acts convex",
      "hyperbolic geometry",
      "fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}