{
  "id": "0706.2175",
  "version": "v1",
  "published": "2007-06-14T18:50:12.000Z",
  "updated": "2007-06-14T18:50:12.000Z",
  "title": "A resolution of the K(2)-local sphere at the prime 3",
  "authors": [
    "P. Goerss",
    "H. -W. Henn",
    "M. Mahowald",
    "C. Rezk"
  ],
  "comment": "46 pages, published version",
  "journal": "Ann. of Math. (2) 162 (2005), no. 2, 777--822",
  "categories": [
    "math.AT"
  ],
  "abstract": "We develop a framework for displaying the stable homotopy theory of the sphere, at least after localization at the second Morava K-theory K(2). At the prime 3, we write the spectrum L_{K(2)S^0 as the inverse limit of a tower of fibrations with four layers. The successive fibers are of the form E_2^hF where F is a finite subgroup of the Morava stabilizer group and E_2 is the second Morava or Lubin-Tate homology theory. We give explicit calculation of the homotopy groups of these fibers. The case n=2 at p=3 represents the edge of our current knowledge: n=1 is classical and at n=2, the prime 3 is the largest prime where the Morava stabilizer group has a p-torsion subgroup, so that the homotopy theory is not entirely algebraic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-14T18:50:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55Q45",
      "55P60"
    ],
    "keywords": [
      "morava stabilizer group",
      "resolution",
      "second morava k-theory",
      "lubin-tate homology theory",
      "p-torsion subgroup"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.2175G"
    }
  }
}