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On the geometric quantization of the symplectic leaves of Poisson manifolds

✍ Scribed by Izu Vaisman

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 861 KB
Volume: 7
Category: Article
ISSN: 0926-2245
DOI: 10.1016/s0926-2245(96)00056-3

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✦ Synopsis

In the paper, we establish some conditions which ensure one of the following: (i) the existence of the pullback of the quantization bundle of a Poisson manifold to a quantization bundle of a symplectic leaf, (ii) the existence of the projection of a quantization bundle from a presymplectic realization of a Poisson manifold to the manifold or to its symplectic leaves. The main case is that of an isotropic realization. The paper ends by a discussion of the notion of a polarization of a Poisson manifold.

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