{
  "id": "math/0112169",
  "version": "v1",
  "published": "2001-12-17T16:02:57.000Z",
  "updated": "2001-12-17T16:02:57.000Z",
  "title": "Subalgebras of group cohomology defined by infinite loop spaces",
  "authors": [
    "John R. Hunton",
    "Bjorn Schuster"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "We study natural subalgebras Ch_E(G) of group cohomology defined in terms of infinite loop spaces E and give representation theoretic descriptions of those based on QS^0 and the Johnson-Wilson theories E(n). We describe the subalgebras arising from the Brown-Peterson spectra BP and as a result give a simple reproof of Yagita's theorem that the image of BP^*(BG) in H^*(BG;F_p) is F-isomorphic to the whole cohomology ring; the same result is shown to hold with BP replaced by any complex oriented theory E with a map of ring spectra from E to HF_p which is non-trivial in homotopy. We also extend the constructions to define subalgebras of H^*(X;F_p) for any space X; when X is finite we show that the subalgebras Ch_{E(n)}(X) give a natural unstable chromatic filtration of H^*(X;F_p).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-12-17T16:02:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J06",
      "55P47"
    ],
    "keywords": [
      "infinite loop spaces",
      "group cohomology",
      "study natural subalgebras",
      "natural unstable chromatic filtration",
      "representation theoretic descriptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....12169H"
    }
  }
}