{
  "id": "0902.4867",
  "version": "v1",
  "published": "2009-02-27T16:45:01.000Z",
  "updated": "2009-02-27T16:45:01.000Z",
  "title": "Completed representation ring spectra of nilpotent groups",
  "authors": [
    "Tyler Lawson"
  ],
  "comment": "This is the version published by Algebraic & Geometric Topology on 26 February 2006",
  "journal": "Algebr. Geom. Topol. 6 (2006) 253-285",
  "doi": "10.2140/agt.2006.6.253",
  "categories": [
    "math.AT",
    "math.GR"
  ],
  "abstract": "In this paper, we examine the `derived completion' of the representation ring of a pro-p group G_p^ with respect to an augmentation ideal. This completion is no longer a ring: it is a spectrum with the structure of a module spectrum over the Eilenberg-MacLane spectrum HZ, and can have higher homotopy information. In order to explain the origin of some of these higher homotopy classes, we define a deformation representation ring functor R[-] from groups to ring spectra, and show that the map R[G_p^] --> R[G] becomes an equivalence after completion when G is finitely generated nilpotent. As an application, we compute the derived completion of the representation ring of the simplest nontrivial case, the p-adic Heisenberg group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-27T16:45:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P60",
      "19A22",
      "55P43"
    ],
    "keywords": [
      "completed representation ring spectra",
      "nilpotent groups",
      "simplest nontrivial case",
      "higher homotopy information",
      "deformation representation ring functor"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.4867L"
    }
  }
}