{
  "id": "0903.2871",
  "version": "v1",
  "published": "2009-03-16T22:58:31.000Z",
  "updated": "2009-03-16T22:58:31.000Z",
  "title": "De Rham cohomology of diffeological spaces and foliations",
  "authors": [
    "G. Hector",
    "E. Macías-Virgós",
    "E. Sanmartín-Carbón"
  ],
  "comment": "13 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $(M,\\mathcal{F})$ be a foliated manifold. We prove that there is a canonical isomorphism between the complex of base-like forms $\\Omega^*_b(M,\\mathcal{F})$ of the foliation and the \"De Rham complex\" of the space of leaves $M/\\mathcal{F}$ when considered as a \"diffeological\" quotient. Consequently, the two corresponding cohomology groups $H^*_b(M,\\mathcal{F})$ and $H^*(M/\\mathcal{F})$ are isomorphic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-16T22:58:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R30",
      "58B99"
    ],
    "keywords": [
      "rham cohomology",
      "diffeological spaces",
      "rham complex",
      "corresponding cohomology groups",
      "foliated manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.2871H"
    }
  }
}