{
  "id": "1404.3847",
  "version": "v1",
  "published": "2014-04-15T08:47:16.000Z",
  "updated": "2014-04-15T08:47:16.000Z",
  "title": "Teichmuller spaces, ergodic theory and global Torelli theorem",
  "authors": [
    "Misha Verbitsky"
  ],
  "comment": "21 pages, ICM submission",
  "categories": [
    "math.AG"
  ],
  "abstract": "A Teichm\\\"uller space $Teich$ is a quotient of the space of all complex structures on a given manifold $M$ by the connected components of the group of diffeomorphisms. The mapping class group $\\Gamma$ of $M$ is the group of connected components of the diffeomorphism group. The moduli problems can be understood as statements about the $\\Gamma$-action on $Teich$. I will describe the mapping class group and the Teichmuller space for a hyperkahler manifold. It turns out that this action is ergodic. We use the ergodicity to show that a hyperkahler manifold is never Kobayashi hyperbolic. This is my ICM submission, with review of some of my work on Teichmuller spaces and moduli; proofs are sketched, new observations and some open problems added.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-15T08:47:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G13",
      "53C26"
    ],
    "keywords": [
      "teichmuller space",
      "global torelli theorem",
      "ergodic theory",
      "mapping class group",
      "hyperkahler manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.3847V"
    }
  }
}