Integrability of Poisson brackets

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We show that various notions of integrability for Poisson brackets are all equivalent, and we give the precise obstructions to integrating Poisson manifolds. We describe the integration as a symplectic quotient, in the spirit of the Poisson sigma-model of Cattaneo and Felder. For regular Poisson manifolds we express the obstructions in terms of variations of symplectic areas. As an application of these results, we show that a Poisson manifold admits a complete symplectic realization if, and only if, it is integrable. We discuss also the integration of submanifolds and Morita equivalence of Poisson manifolds.
43 pages, 1 figure

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Differential Geometry, Geometric Topology, Symplectic Geometry, 53D17

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http://salesiana.dossiersoluciones.com/handle/123456789/65241

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0210152
 http://arxiv.org/abs/math/0210152

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arXiv