{
  "id": "math/0009038",
  "version": "v1",
  "published": "2000-09-04T16:54:20.000Z",
  "updated": "2000-09-04T16:54:20.000Z",
  "title": "Hodge theory on hyperbolic manifolds of infinite volume",
  "authors": [
    "Martin Olbrich"
  ],
  "comment": "9 pages, to appear in the Proceedings of \"Lie Theory and Its Applications in Physics - Lie III\" (World Scientific, 2000)",
  "categories": [
    "math.DG",
    "math.RT"
  ],
  "abstract": "Let $Y=\\Gamma\\backslash H^n$ be a quotient of the hyperbolic space by the action of a discrete convex-cocompact group of isometries. We describe certain spaces of $\\Gamma$-invariant currents on the sphere at infinity of $H^n$ with support on the limit set of $\\Gamma$. These spaces are finite-dimensional. The main result identifies the cohomology of $Y$ with a quotient of such spaces. We explain in which sense this result generalizes the classical Hodge theorem for compact quotients. We obtain analogous results for the cohomology groups $H^p(\\Gamma,F)$, where $F$ is a finite-dimensional representation of the full group of orientation preserving isometries of $H^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-09-04T16:54:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40"
    ],
    "keywords": [
      "hyperbolic manifolds",
      "infinite volume",
      "hodge theory",
      "discrete convex-cocompact group",
      "main result identifies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......9038O"
    }
  }
}