{
  "id": "0905.3121",
  "version": "v1",
  "published": "2009-05-19T14:57:27.000Z",
  "updated": "2009-05-19T14:57:27.000Z",
  "title": "The computation of Stiefel-Whitney classes",
  "authors": [
    "Pierre Guillot"
  ],
  "comment": "To appear in Ann. Inst. Fourier",
  "categories": [
    "math.AT"
  ],
  "abstract": "The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here \"compute\" means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet). Next, we give an application: thanks to the new information gathered, we can in many cases determine which cohomology classes are supported by algebraic varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-19T14:57:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J06",
      "57R20",
      "65K05",
      "14C15"
    ],
    "keywords": [
      "stiefel-whitney classes",
      "computation",
      "finite group",
      "algebraic varieties",
      "finite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.3121G"
    }
  }
}