{
  "id": "math/0605249",
  "version": "v3",
  "published": "2006-05-10T07:15:45.000Z",
  "updated": "2010-09-21T22:56:47.000Z",
  "title": "The homotopy type of the cobordism category",
  "authors": [
    "Soren Galatius",
    "Ib Madsen",
    "Ulrike Tillmann",
    "Michael Weiss"
  ],
  "comment": "40 pages. v2 has improved notation, added explanations, and minor mistakes fixed. v3 has minor corrections and improvements. Final submitted version",
  "journal": "Acta Math. 202 (2009), no. 2, 195--239",
  "categories": [
    "math.AT"
  ],
  "abstract": "The embedded cobordism category under study in this paper generalizes the category of conformal surfaces, introduced by G. Segal in order to formalize the concept of field theories. Our main result identifies the homotopy type of the classifying space of the embedded d-dimensional cobordism category for all d. For d=2, our results lead to a new proof of the generalized Mumford conjecture, somewhat different in spirit from the original one.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-09-21T22:56:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R90"
    ],
    "keywords": [
      "homotopy type",
      "embedded d-dimensional cobordism category",
      "main result identifies",
      "paper generalizes",
      "conformal surfaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5249G"
    }
  }
}