{
  "id": "2108.13084",
  "version": "v1",
  "published": "2021-08-30T09:40:11.000Z",
  "updated": "2021-08-30T09:40:11.000Z",
  "title": "Local systems in diffeology",
  "authors": [
    "Katsuhiko Kuribayashi"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AT",
    "math.DG",
    "math.KT"
  ],
  "abstract": "By using local systems over simplicial sets with values in differential graded algebras, we consider a framework of rational and ${\\mathbb R}$-local homotopy theory for diffeological spaces with arbitrary fundamental groups. Moreover, a spectral sequence converging to the singular de Rham cohomology of an adjunction space is constructed with the pullback of local systems. In case of a stratifold obtained by attaching manifolds, the spectral sequence converges to the original de Rham cohomology, which is due to Souriau, of the stratifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-30T09:40:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local systems",
      "diffeology",
      "rham cohomology",
      "local homotopy theory",
      "arbitrary fundamental groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}