Morita equivalence and symplectic realizations of Poisson manifolds
Ping Xu (1992)
Annales scientifiques de l'École Normale Supérieure
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Ping Xu (1992)
Annales scientifiques de l'École Normale Supérieure
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Nguyen Tien Zung (2006)
Annales scientifiques de l'École Normale Supérieure
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Marius Crainic, Chenchang Zhu (2007)
Annales de l’institut Fourier
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We discuss the integrability of Jacobi manifolds by contact groupoids, and then look at what the Jacobi point of view brings new into Poisson geometry. In particular, using contact groupoids, we prove a Kostant-type theorem on the prequantization of symplectic groupoids, which answers a question posed by Weinstein and Xu. The methods used are those of Crainic-Fernandes on -paths and monodromy group(oid)s of algebroids. In particular, most of the results we obtain are valid also in the...
Ping Xu (1992)
Annales de l'institut Fourier
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The main purpose of this paper is to suggest a method of computing Poisson cohomology of a Poisson manifold by means of symplectic groupoids. The key idea is to convert the problem of computing Poisson cohomology to that of computing de Rham cohomology of certain manifolds. In particular, we shall derive an explicit formula for the Poisson cohomology of a regular Poisson manifold where the symplectic foliation is a trivial fibration.
Piotr Stachura (2000)
Banach Center Publications
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Kirill Mackenzie (1987)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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P. Heinzner, F. Loose, A. Huckleberry (1994)
Journal für die reine und angewandte Mathematik
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Francesco Bonechi (2015)
Banach Center Publications
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We discuss the role of Poisson-Nijenhuis (PN) geometry in the definition of multiplicative integrable models on symplectic groupoids. These are integrable models that are compatible with the groupoid structure in such a way that the set of contour levels of the hamiltonians in involution inherits a topological groupoid structure. We show that every maximal rank PN structure defines such a model. We consider the examples defined on compact hermitian symmetric spaces studied by F. Bonechi,...
Z.J. Liu, P. Xu (1996)
Geometric and functional analysis
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