Obstruction classes of crossed modules of Lie algebroids and Lie groupoids linked to existence of principal bundles
| dc.creator | Laurent-Gengoux, Camille | |
| dc.creator | Wagemann, Friedrich | |
| dc.date | 2006-11-08 | |
| dc.date | 2007-03-19 | |
| dc.date.accessioned | 2026-07-07T10:00:27Z | |
| dc.date.available | 2026-07-07T10:00:27Z | |
| dc.description | Let K be a Lie group and P be a K-principal bundle on a manifold M. Suppose given furthermore a central extension 1\to Z\to \hat{K}\to K\to 1 of K. It is a classical question whether there exists a \hat{K}-principal bundle \hat{P} on M such that \hat{P}/Z is isomorphic to P. Neeb defines in this context a crossed module of topological Lie algebras whose cohomology class [ω_{\rm top alg}] is an obstruction to the existence of \hat{P}. In the present paper, we show that [ω_{\rm top alg}] is up to torsion a full obstruction for this problem, and we clarify its relation to crossed modules of Lie algebroids and Lie groupoids, and finally to gerbes. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611226 | |
| dc.identifier | http://arxiv.org/abs/math/0611226 | |
| dc.identifier | Annals of Global Analysis and Geometry 34 (2007) 21--37 | |
| dc.identifier | doi:10.1007/s10455-007-9098-0 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168328 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 22A22, 17B56, 18F20, 18G40 | |
| dc.title | Obstruction classes of crossed modules of Lie algebroids and Lie groupoids linked to existence of principal bundles | |
| dc.type | text |