{
  "id": "1310.2907",
  "version": "v1",
  "published": "2013-10-10T18:29:22.000Z",
  "updated": "2013-10-10T18:29:22.000Z",
  "title": "Representations of 3-manifold groups in PGL(n,C) and their restriction to the boundary",
  "authors": [
    "Antonin Guilloux"
  ],
  "comment": "24 pages, 5 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study here the space of representations of a fundamental group of a 3-manifold into PGL(n,C). Thurston, Neumann and Zagier initiated a strategy (in the case of PGL(2,C)) consisting in: triangulate the manifold, assign shapes to each pieces and then try to glue back. This leads to the \"gluing equations\" and the Neumann-Zagier symplectic space. Building on the works of Dimofte-Gabella-Goncharov and Bergeron-Falbel-Guilloux, we complete the picture in the case of PGL(n,C). We recover a situation very similar to the case of PGL(2,C). This allows for example to obtain a combinatorial proof of a local rigidity results for such representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-10T18:29:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "representations",
      "restriction",
      "neumann-zagier symplectic space",
      "local rigidity results",
      "fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.2907G"
    }
  }
}