{
  "id": "1504.03191",
  "version": "v1",
  "published": "2015-04-13T14:08:04.000Z",
  "updated": "2015-04-13T14:08:04.000Z",
  "title": "Cohomology with twisted coefficients of the classifying space of a fusion system",
  "authors": [
    "Rémi Molinier"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AT",
    "math.GR"
  ],
  "abstract": "We study the cohomology with twisted coefficients of the geometric realization of a linking system associated to a saturated fusion system $\\mathcal{F}$. More precisely, we extend a result due to Broto, Levi and Oliver to twisted coefficients. We generalize the notion of $\\mathcal{F}$-stable elements to $\\mathcal{F}^c$-stable elements in a setting of twisted coefficient cohomology and we show that, if the coefficient module is nilpotent, then the cohomology of the geometric realization of a linking system can be computed by $\\mathcal{F}^c$-stable elements. As a corollary, we show that for any coefficient module, the cohomology of the classifying space of a $p$-local finite group can be computed by these $\\mathcal{F}^c$-stable elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-13T14:08:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R40",
      "55N25",
      "55R35",
      "20J06",
      "20D20",
      "20J15"
    ],
    "keywords": [
      "classifying space",
      "stable elements",
      "geometric realization",
      "coefficient module",
      "linking system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150403191M"
    }
  }
}