{
  "id": "math/0109031",
  "version": "v3",
  "published": "2001-09-05T05:43:27.000Z",
  "updated": "2003-06-12T20:20:58.000Z",
  "title": "Cohomology of groups of diffeomorphims related to the modules of differential operators on a smooth manifold",
  "authors": [
    "Sofiane Bouarroudj"
  ],
  "comment": "arxiv version is already official",
  "journal": "J. Nonlinear Math. Phys., volume 9, no. 4 (2002) 455-463",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $M$ be a manifold and $T^*M$ be the cotangent bundle. We introduce a 1-cocycle on the group of diffeomorphisms of $M$ with values in the space of linear differential operators acting on $C^{\\infty} (T^*M).$ When $M$ is the $n$-dimensional sphere, $S^n$, we use this 1-cocycle to compute the first-cohomology group of the group of diffeomorphisms of $S^n$, with coefficients in the space of linear differential operators acting on contravariant tensor fields.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-06-12T20:20:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smooth manifold",
      "diffeomorphims",
      "linear differential operators acting",
      "contravariant tensor fields",
      "cotangent bundle"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.2991/jnmp.2002.9.4.6",
      "journal": "Journal of Nonlinear Mathematical Physics",
      "year": 2002,
      "volume": 9,
      "number": 4,
      "pages": 455
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002JNMP....9..455B"
    }
  }
}