Intégration symplectique des variétés de Poisson régulières
| dc.creator | Alcalde-Cuesta, F. | |
| dc.creator | Hector, G. | |
| dc.date | 1994-07-20 | |
| dc.date.accessioned | 2026-07-07T09:12:23Z | |
| dc.date.available | 2026-07-07T09:12:23Z | |
| dc.description | A symplectic integration of a Poisson manifold $(M,Λ)$ is a symplectic groupoid $(Γ,η)$ which realizes the given Poisson manifold, i.e. such that the space of units $Γ_0$ with the induced Poisson structure $Λ_0$ is isomorphic to $(M,Λ)$. This notion was introduced by A. Weinstein in order to quantize Poisson manifolds by quantizing their symplectic integration. Any Poisson manifold can be integrated by a local symplectic groupoid but already for regular Poisson manifolds there are obstructions to global integrability. The aim of this paper is to summarize all the known obstructions and present a sufficient topological condition for integrability of regular Poisson manifolds; we will indeed describe a concrete procedure for this integration. Further our criterion will provide necessary and sufficient if we require $Γ$ to be Hausdorff, which is a suitable condition to proceed to Weinstein's program of quantization. These integrability results may be interpreted as an generalization of the Cartan-Smith proof of Lie's third theorem in the infinite dimensional case. | |
| dc.description | 39 pages, LATEX | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9407009 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9407009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152006 | |
| dc.subject | Differential Geometry | |
| dc.title | Intégration symplectique des variétés de Poisson régulières | |
| dc.type | text |