{
  "id": "math/0609635",
  "version": "v3",
  "published": "2006-09-22T10:45:56.000Z",
  "updated": "2008-06-15T16:31:49.000Z",
  "title": "Equivariant homotopy theory for pro-spectra",
  "authors": [
    "Halvard Fausk"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The G-homotopy theory is \"pieced together\" from the G/U-homotopy theories for suitable quotient groups G/U of G; a motivation is the way continuous group cohomology of a profinite group is built out of the cohomology of its finite quotient groups. In the model category of equivariant spectra Postnikov towers are studied from a general perspective. We introduce pro-G-spectra and construct various model structures on them. A key property of the model structures is that pro-spectra are weakly equivalent to their Postnikov towers. We discuss two versions of a model structure with \"underlying weak equivalences\". One of the versions only makes sense for pro-spectra. In the end we use the theory to study homotopy fixed points of pro-G-spectra.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-06-15T16:31:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P91",
      "18G55"
    ],
    "keywords": [
      "equivariant homotopy theory",
      "pro-spectra",
      "model structure",
      "profinite group",
      "equivariant spectra postnikov towers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9635F"
    }
  }
}