{
  "id": "2007.13285",
  "version": "v1",
  "published": "2020-07-27T02:49:14.000Z",
  "updated": "2020-07-27T02:49:14.000Z",
  "title": "Symplectic coordinates on the deformation spaces of convex projective structures on 2-orbifolds",
  "authors": [
    "Suhyoung Choi",
    "Hongtaek Jung"
  ],
  "comment": "40 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $\\mathcal{O}$ be a closed orientable 2-orbifold of negative Euler characteristic that has only cone singularities. Huebschmann constructed the Atiyah-Bott-Goldman type symplectic form $\\omega$ on the deformation space $\\mathcal{C}(\\mathcal{O})$ of convex projective structures on $\\mathcal{O}$. We show that the deformation space $\\mathcal{C}(\\mathcal{O})$ of convex projective structures on $\\mathcal{O}$ admits a global Darboux coordinates system with respect to $\\omega$. To this end, we show that $\\mathcal{C}(\\mathcal{O})$ can be decomposed into smaller symplectic spaces. In the course of the proof, we also study the deformation space $\\mathcal{C}(\\mathcal{O})$ for an orbifold $\\mathcal{O}$ with boundary and construct the symplectic form on the deformation space of convex projective structures on $\\mathcal{O}$ with fixed boundary holonomy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-27T02:49:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57K20",
      "53D05"
    ],
    "keywords": [
      "convex projective structures",
      "deformation space",
      "symplectic coordinates",
      "atiyah-bott-goldman type symplectic form",
      "global darboux coordinates system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}