{
  "id": "0710.5426",
  "version": "v2",
  "published": "2007-10-29T13:41:30.000Z",
  "updated": "2008-08-12T18:59:52.000Z",
  "title": "On the existence of a v_2^32-self map on M(1,4) at the prime 2",
  "authors": [
    "Mark Behrens",
    "Michael Hill",
    "Michael J. Hopkins",
    "Mark Mahowald"
  ],
  "comment": "31 pages, 16 figures. Revised version: includes new section (section 9)explaining centrality of d_2(v_2^8) and d_3(v_2^16), and fixes an error in section 7",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let M(1) be the mod 2 Moore spectrum. J.F. Adams proved that M(1) admits a minimal v_1-self map v_1^4: Sigma^8 M(1) -> M(1). Let M(1,4) be the cofiber of this self-map. The purpose of this paper is to prove that M(1,4) admits a minimal v_2-self map of the form v_2^32: Sigma^192 M(1,4) -> M(1,4). The existence of this map implies the existence of many 192-periodic families of elements in the stable homotopy groups of spheres.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-12T18:59:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q51",
      "55Q40"
    ],
    "keywords": [
      "moore spectrum",
      "map implies",
      "stable homotopy groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.5426B"
    }
  }
}