Abstract
The theory of principal G-bundles over a Lie groupoid is an important one unifying 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 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(g*)G → H* (BG) when the manifold is a point.
Original language | English (US) |
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Pages (from-to) | 451-491 |
Number of pages | 41 |
Journal | Mathematische Zeitschrift |
Volume | 255 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2007 |
All Science Journal Classification (ASJC) codes
- General Mathematics