Differentiable Stacks and Gerbes
| dc.creator | Behrend, Kai | |
| dc.creator | Xu, Ping | |
| dc.date | 2006-05-27 | |
| dc.date | 2008-12-31 | |
| dc.date.accessioned | 2026-07-07T12:23:29Z | |
| dc.date.available | 2026-07-07T12:23:29Z | |
| dc.description | We introduce differentiable stacks and explain the relationship with Lie groupoids. Then we study $S^1$-bundles and $S^1$-gerbes over differentiable stacks. In particular, we establish the relationship between $S^1$-gerbes and groupoid $S^1$-central extensions. We define connections and curvings for groupoid $S^1$-central extensions extending the corresponding notions of Brylinski, Hitchin and Murray for $S^1$-gerbes over manifolds. We develop a Chern-Weil theory of characteristic classes in this general setting by presenting a construction of Chern classes and Dixmier-Douady classes in terms of analogues of connections and curvatures. We also describe a prequantization result for both $S^1$-bundles and $S^1$-gerbes extending the well-known result of Weil and Kostant. In particular, we give an explicit construction of $S^1$-central extensions with prescribed curvature-like data. | |
| dc.description | 48 pages, minor revision, examples added, references added and updated | |
| dc.identifier | https://arxiv.org/abs/math/0605694 | |
| dc.identifier | http://arxiv.org/abs/math/0605694 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214005 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.title | Differentiable Stacks and Gerbes | |
| dc.type | text |