{
  "id": "2002.06802",
  "version": "v1",
  "published": "2020-02-17T06:49:54.000Z",
  "updated": "2020-02-17T06:49:54.000Z",
  "title": "A comparison between two de Rham complexes in diffeology",
  "authors": [
    "Katsuhiko Kuribayashi"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AT",
    "math.DG",
    "math.KT"
  ],
  "abstract": "There are two de Rham complexes in diffeology. The original one is due to Souriau and another one is the singular de Rham complex defined by a simplicial differential graded algebra. We compare the first de Rham cohomology groups of the two complexes within the \\v{C}ech--de Rham spectral sequence in diffeology. In particular, a comparison map enables us to conclude that the first singular de Rham cohomology for the irrational torus $T_\\theta$ is isomorphic to the direct sum of the original one and the group of equivalence classes of flow bundles over $T_\\theta$ with connection $1$-forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-17T06:49:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rham complex",
      "diffeology",
      "simplicial differential graded algebra",
      "rham cohomology groups",
      "rham spectral sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}