Chern-Weil map for principal bundles over groupoids

Camille Laurent-Gengoux, Jean Louis Tu, Ping Xu

Research output: Contribution to journalArticle

13 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)451-491
Number of pages41
JournalMathematische Zeitschrift
Volume255
Issue number3
DOIs
StatePublished - Mar 1 2007

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Principal Bundle
Groupoids
Bundle
Characteristic Classes
Equivariant
Equivariant Cohomology
Holonomy
Groupoid
Orbifold
Differential Geometry
Model

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Laurent-Gengoux, Camille ; Tu, Jean Louis ; Xu, Ping. / Chern-Weil map for principal bundles over groupoids. In: Mathematische Zeitschrift. 2007 ; Vol. 255, No. 3. pp. 451-491.
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Chern-Weil map for principal bundles over groupoids. / Laurent-Gengoux, Camille; Tu, Jean Louis; Xu, Ping.

In: Mathematische Zeitschrift, Vol. 255, No. 3, 01.03.2007, p. 451-491.

Research output: Contribution to journalArticle

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