Journal of Differential Geometry

Integrability of Poisson Brackets

Marius Crainic and Rui Loja Fernandes

Full-text: Open access

Abstract

We discuss the integration of Poisson brackets, motivated by our recent solution to the integrability problem for general Lie brackets. We give the precise obstructions to integrating Poisson manifolds, describing 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, improving on results of Alcalde Cuesta and Hector. We apply our results (and our point of view) to decide about the existence of complete symplectic realizations, to the integrability of submanifolds of Poisson manifolds, and to the study of dual pairs, Morita equivalence and reduction.

Article information

Source
J. Differential Geom., Volume 66, Number 1 (2004), 71-137.

Dates
First available in Project Euclid: 21 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090415030

Digital Object Identifier
doi:10.4310/jdg/1090415030

Mathematical Reviews number (MathSciNet)
MR2128714

Zentralblatt MATH identifier
1066.53131

Citation

Crainic, Marius; Fernandes, Rui Loja. Integrability of Poisson Brackets. J. Differential Geom. 66 (2004), no. 1, 71--137. doi:10.4310/jdg/1090415030. https://projecteuclid.org/euclid.jdg/1090415030


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