Chern-Weil map for principal bundles over groupoids
| dc.creator | Laurent-Gengoux, Camille | |
| dc.creator | Tu, Jean-Louis | |
| dc.creator | Xu, Ping | |
| dc.date | 2004-01-29 | |
| dc.date | 2006-02-10 | |
| dc.date.accessioned | 2026-07-07T06:35:57Z | |
| dc.date.available | 2026-07-07T06:35:57Z | |
| dc.description | 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. | |
| dc.description | 43 pages. References added, typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0401420 | |
| dc.identifier | http://arxiv.org/abs/math/0401420 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99949 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | 58F05 | |
| dc.title | Chern-Weil map for principal bundles over groupoids | |
| dc.type | text |