{
  "id": "math/0507076",
  "version": "v2",
  "published": "2005-07-04T17:51:28.000Z",
  "updated": "2009-02-18T15:28:51.000Z",
  "title": "Pontryagin forms on $(4k-2)$-manifolds and symplectic structures on the spaces of Riemannian metrics",
  "authors": [
    "Roberto Ferreiro Perez",
    "Jaime Muñoz Masque"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "The Pontryagin forms on 1-jet bundle of Riemannian metrics, are shown to provide, in a natural way, diffeomorphism-invariant pre-symplectic structures on the space of Riemannian metrics for dimensions $n=4r-2$. The equivariant Pontryagin forms provide canonical moment maps for these structures. In dimension two, the symplectic reduction corresponding to the pre-symplectic form and its moment map attached to the first Pontryagin form, is proved to coincide with the Teichm\\\"{u}ller space endowed with the Weil-Petersson symplectic form.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-02-18T15:28:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D30",
      "55R40",
      "58A20",
      "58D17"
    ],
    "keywords": [
      "riemannian metrics",
      "first pontryagin form",
      "weil-petersson symplectic form",
      "equivariant pontryagin forms",
      "diffeomorphism-invariant pre-symplectic structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7076F"
    }
  }
}