On the geometric quantization of the symplectic leaves of poisson manifolds

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Abstract

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.

Original languageEnglish
Pages (from-to)265-275
Number of pages11
JournalDifferential Geometry and its Application
Volume7
Issue number3
DOIs
StatePublished - Sep 1997

Keywords

  • Poisson manifold
  • Polarization
  • Presymplectic manifold
  • Quantization triple

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Computational Theory and Mathematics

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