{
  "id": "1112.4357",
  "version": "v2",
  "published": "2011-12-19T15:04:47.000Z",
  "updated": "2012-03-07T07:38:49.000Z",
  "title": "Conjugation spaces and equivariant Chern classes",
  "authors": [
    "W. Pitsch",
    "J. Scherer"
  ],
  "comment": "15 pages. This new version corrects the receptacle for the equivariant Chern classes of Real bundles by twisting the coefficients. When n is odd, we use the sign representation of C_2 on the integers, when n is even the action is trivial",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "Let h be a Real bundle, in the sense of Atiyah, over a space X. This is a complex vector bundle together with an involution which is compatible with complex conjugation. We use the fact that BU is equipped with a structure of conjugation space, as defined by Hausmann, Holm, and Puppe, to construct equivariant Chern classes in the Z/2-equivariant cohomology of X with twisted integer coefficients. We show that these classes determine the (non-equivariant) Chern classes of h, forgetting the involution on X, and the Stiefel-Whitney classes of the real bundle of fixed points.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-07T07:38:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R20",
      "55N91",
      "55N15",
      "55P92",
      "55R10"
    ],
    "keywords": [
      "conjugation space",
      "real bundle",
      "complex vector bundle",
      "construct equivariant chern classes",
      "complex conjugation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.4357P"
    }
  }
}