{
  "id": "1912.10544",
  "version": "v1",
  "published": "2019-12-22T21:28:11.000Z",
  "updated": "2019-12-22T21:28:11.000Z",
  "title": "Classifying spaces of infinity-sheaves",
  "authors": [
    "Daniel Berwick-Evans",
    "Pedro Boavida de Brito",
    "Dmitri Pavlov"
  ],
  "comment": "31 pages. Comments are very welcome",
  "categories": [
    "math.AT",
    "math.CT",
    "math.KT"
  ],
  "abstract": "We prove that the set of concordance classes of sections of an infinity-sheaf on a manifold is representable, extending a theorem of Madsen and Weiss. This is reminiscent of an h-principle in which the role of isotopy is played by concordance. As an application, we offer an answer to the question: what does the classifying space of a Segal space classify?",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-22T21:28:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N30",
      "57R19",
      "55N20",
      "18G60",
      "22A22",
      "18F10",
      "18F20",
      "14D23",
      "14A20",
      "58D27",
      "58D29",
      "14D22",
      "55R35",
      "55U35",
      "18G55",
      "14F42",
      "55R65"
    ],
    "keywords": [
      "classifying space",
      "infinity-sheaf",
      "concordance classes",
      "reminiscent",
      "h-principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}