{
  "id": "math/0611808",
  "version": "v3",
  "published": "2006-11-27T09:16:24.000Z",
  "updated": "2007-10-15T06:34:21.000Z",
  "title": "Universal Toda brackets of ring spectra",
  "authors": [
    "Steffen Sagave"
  ],
  "comment": "38 pages; a few typos corrected, to appear in Trans. Amer. Math. Soc",
  "journal": "Trans. Amer. Math. Soc., 360(5):2767-2808, 2008.",
  "doi": "10.1090/S0002-9947-07-04487-X",
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "We construct and examine the universal Toda bracket of a highly structured ring spectrum R. This invariant of R is a cohomology class in the Mac Lane cohomology of the graded ring of homotopy groups of R which carries information about R and the category of R-module spectra. It determines for example all triple Toda brackets of R and the first obstruction to realizing a module over the homotopy groups of R by an R-module spectrum. For periodic ring spectra, we study the corresponding theory of higher universal Toda brackets. The real and complex K-theory spectra serve as our main examples.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-10-15T06:34:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P43",
      "19D55",
      "55S35",
      "55U35"
    ],
    "keywords": [
      "ring spectrum",
      "complex k-theory spectra serve",
      "r-module spectrum",
      "homotopy groups",
      "higher universal toda brackets"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11808S"
    }
  }
}