{
  "id": "1208.3370",
  "version": "v1",
  "published": "2012-08-16T13:54:02.000Z",
  "updated": "2012-08-16T13:54:02.000Z",
  "title": "A geometric interpretation of the homotopy groups of the cobordism category",
  "authors": [
    "Marcel Bökstedt",
    "Anne Marie Svane"
  ],
  "comment": "23 pages",
  "doi": "10.1093/qmath/hau011",
  "categories": [
    "math.AT"
  ],
  "abstract": "The classifying space of the embedded cobordism category has been identified in by Galatius, Tillmann, Madsen, and Weiss as the infinite loop space of a certain Thom spectrum. This identifies the set of path components with the classical cobordism group. In this paper, we give a geometric interpretation of the higher homotopy groups as certain cobordism groups where all manifolds are now equipped with a set of orthonormal sections in the tangent bundle. We also give a description of the fundamental group as a free group with a set of geometrically intuitive relations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-16T13:54:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R90"
    ],
    "keywords": [
      "geometric interpretation",
      "higher homotopy groups",
      "infinite loop space",
      "embedded cobordism category",
      "path components"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.3370B"
    }
  }
}