{
  "id": "1001.0771",
  "version": "v3",
  "published": "2010-01-05T21:31:15.000Z",
  "updated": "2011-04-01T15:16:34.000Z",
  "title": "Completion of $G$-spectra and stable maps between classifying spaces",
  "authors": [
    "Kári Ragnarsson"
  ],
  "comment": "Final version, to appear in Advances in Mathematics",
  "doi": "10.1016/j.aim.2011.03.014",
  "categories": [
    "math.AT"
  ],
  "abstract": "We prove structural theorems for computing the completion of a G-spectrum at the augmentation ideal of the Burnside ring of a finite group G. First we show that a G-spectrum can be replaced by a spectrum obtained by allowing only isotropy groups of prime power order without changing the homotopy type of the completion. We then show that this completion can be computed as a homotopy colimit of completions of spectra obtained by further restricting isotropy to one prime at a time, and that these completions can be computed in terms of completion at a prime. As an application, we show that the spectrum of stable maps from BG to the classifying space of a compact Lie group K splits non-equivariantly as a wedge sum of p-completed suspension spectra of classifying spaces of certain subquotients of the product of G and K. In particular this describes the dual of BG.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-04-01T15:16:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P42",
      "55R39",
      "55P60",
      "55P91"
    ],
    "keywords": [
      "classifying space",
      "completion",
      "stable maps",
      "compact lie group",
      "prime power order"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.0771R"
    }
  }
}