{
  "id": "math/0401420",
  "version": "v3",
  "published": "2004-01-29T20:07:01.000Z",
  "updated": "2006-02-10T09:44:43.000Z",
  "title": "Chern-Weil map for principal bundles over groupoids",
  "authors": [
    "Camille Laurent-Gengoux",
    "Jean-Louis Tu",
    "Ping Xu"
  ],
  "comment": "43 pages. References added, typos corrected",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The theory of principal $G$-bundles over a Lie groupoid is an important one, unifying the various types of principal $G$-bundles, including those over manifolds, those over orbifolds, as well as equivariant principal $G$-bundles. In this paper, we study the differential geometry of these objects, including connections and holonomy maps. We also introduce a Chern-Weil map for these principal bundles and prove that the characteristic classes obtained coincide with the universal characteristic classes. As an application, we recover the equivariant Chern-Weil map of Bott-Tu. We also obtain an explicit chain map between the Weil model and the simplicial model of equivariant cohomology which reduces to the Bott-Shulman map $S({\\mathfrak g}^*)^G \\to H^*(BG)$ when the manifold is a point.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-02-10T09:44:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58F05"
    ],
    "keywords": [
      "principal bundles",
      "explicit chain map",
      "equivariant chern-weil map",
      "universal characteristic classes",
      "equivariant principal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1420L"
    }
  }
}