Open Access
January, 2004 Integrability of Poisson Brackets
Marius Crainic, Rui Loja Fernandes
J. Differential Geom. 66(1): 71-137 (January, 2004). DOI: 10.4310/jdg/1090415030


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.


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Marius Crainic. Rui Loja Fernandes. "Integrability of Poisson Brackets." J. Differential Geom. 66 (1) 71 - 137, January, 2004.


Published: January, 2004
First available in Project Euclid: 21 July 2004

zbMATH: 1066.53131
MathSciNet: MR2128714
Digital Object Identifier: 10.4310/jdg/1090415030

Rights: Copyright © 2004 Lehigh University

Vol.66 • No. 1 • January, 2004
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