Intégration symplectique des variétés de Poisson régulières

Details Intégration symplectique des variétés de Poisson régulières Intégration symplectique des variétés de Poisson régulières

1994-07-20

arxiv.org/abs/dg-ga/9407009v1

Mathematics

Differential Geometry

39 pages, LATEX

Scientific paper

A symplectic integration of a Poisson manifold $(M,\Lambda)$ is a symplectic groupoid $(\Gamma,\eta)$ which realizes the given Poisson manifold, i.e. such that the space of units $\Gamma_0$ with the induced Poisson structure $\Lambda_0$ is isomorphic to $(M,\Lambda)$. 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 $\Gamma$ 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.

Affiliated with

Also associated with

No associations

Rating

Intégration symplectique des variétés de Poisson régulières does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Intégration symplectique des variétés de Poisson régulières, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Intégration symplectique des variétés de Poisson régulières will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-570297