{
  "id": "0803.3205",
  "version": "v1",
  "published": "2008-03-21T17:46:01.000Z",
  "updated": "2008-03-21T17:46:01.000Z",
  "title": "Anick's fibration and the odd primary homotopy exponent of spheres",
  "authors": [
    "Stephen Theriault"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "For primes p>=3, Cohen, Moore, and Neisendorfer showed that the exponent of the p-torsion in the homotopy groups of S^2n+1 is p^n. This was obtained as a consequence of a thorough analysis of the homotopy theory of Moore spaces. Anick further developed this for p>=5 by constructing a homotopy fibration S^2n-1 --> T^2n+1(p^r) --> Loop S^2n+1 whose connecting map is degree p^r on the bottom cell. A much simpler construction of such a fibration for p>=3 was given by Gray and the author using new methods. In this paper the new methods are used to start over, first constructing Anick's fibration for p>=3, and then using it to obtain the exponent result for spheres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-21T17:46:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q40",
      "55R05",
      "55P99"
    ],
    "keywords": [
      "odd primary homotopy exponent",
      "first constructing anicks fibration",
      "homotopy theory",
      "moore spaces",
      "exponent result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.3205T"
    }
  }
}