{
  "id": "1509.02290",
  "version": "v1",
  "published": "2015-09-08T09:16:47.000Z",
  "updated": "2015-09-08T09:16:47.000Z",
  "title": "Six-point configurations in the hyperbolic plane and ergodicity of the mapping class group",
  "authors": [
    "Julien Marché",
    "Maxime Wolff"
  ],
  "comment": "24 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $X$ be the space of isometry classes of ordered sextuples of points in the hyperbolic plane such that the product of the six corresponding rotations of angle $\\pi$ is the identity. This space $X$ is closely related to the PSL$_2(\\mathbb{R})$-character variety of the genus 2 surface $\\Sigma$. In this article we study the topology and the natural symplectic structure on $X$, and we describe the action of the mapping class group of $\\Sigma$ on $X$. This completes the classification of the ergodic components of the character variety in genus 2 initiated in our previous work.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-08T09:16:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M05",
      "20H10",
      "30F60",
      "53D30"
    ],
    "keywords": [
      "mapping class group",
      "hyperbolic plane",
      "six-point configurations",
      "character variety",
      "ergodicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150902290M"
    }
  }
}