{
  "id": "0802.4357",
  "version": "v3",
  "published": "2008-02-29T10:56:14.000Z",
  "updated": "2008-06-25T12:50:46.000Z",
  "title": "Exact sequences of fibrations of crossed complexes, homotopy classification of maps, and nonabelian extensions of groups",
  "authors": [
    "Ronald Brown"
  ],
  "comment": "10 pages, xypic, hyperref 25/06/08 version 2: 12 pages, accepted for JHRS, various minor revisions",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to such a classifying space. This gives results on the homotopy classification of maps from a CW-complex to the classifying space of a crossed module and also, more generally, of a crossed complex whose homotopy groups vanish in dimensions between 1 and n. The results are analogous to those for the obstruction to an abstract kernel in group extension theory.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-06-25T12:50:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13D02",
      "18G50",
      "20J05",
      "55S37",
      "55S45"
    ],
    "keywords": [
      "homotopy classification",
      "crossed complexes",
      "exact sequences",
      "nonabelian extensions",
      "classifying space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.4357B"
    }
  }
}