{
  "id": "math/0107172",
  "version": "v2",
  "published": "2001-07-24T03:54:31.000Z",
  "updated": "2003-07-29T01:45:42.000Z",
  "title": "Geometric structures on orbifolds and holonomy representations",
  "authors": [
    "Suhyoung Choi"
  ],
  "comment": "35 pages",
  "categories": [
    "math.GT",
    "math.GR",
    "math.RA"
  ],
  "abstract": "An orbifold is a topological space modeled on quotient spaces of a finite group actions. We can define the universal cover of an orbifold and the fundamental group as the deck transformation group. Let $G$ be a Lie group acting on a space $X$. We show that the space of isotopy-equivalence classes of $(G,X)$-structures on a compact orbifold $\\Sigma$ is locally homeomorphic to the space of representations of the orbifold fundamental group of $\\Sigma$ to $G$ following the work of Thurston, Morgan, and Lok. This implies that the deformation space of $(G, X)$-structures on $\\Sigma$ is locally homeomorphic to the space of representations of the orbifold fundamental group to $G$ when restricted to the region of proper conjugation action by $G$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-07-29T01:45:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "53A20",
      "53C15"
    ],
    "keywords": [
      "geometric structures",
      "holonomy representations",
      "orbifold fundamental group",
      "proper conjugation action",
      "deck transformation group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......7172C"
    }
  }
}