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Poisson fibrations and fibered symplectic groupoids. (English) Zbl 1158.53064

Dito, Giuseppe (ed.) et al., Poisson geometry in mathematics and physics. Proceedings of the international conference, Tokyo, Japan, June 5–9, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4423-6/pbk). Contemporary Mathematics 450, 41-59 (2008).
A symplectic fibration is a locally trivial fibration with fiber type a symplectic manifold, admitting a collection of trivializations whose transition functions are symplectomorphisms. A Poisson fibration, that is more general than a symplectic fibration, is a locally trivial fibration with fiber type a Poisson manifold, admitting a collection of trivializations whose transition functions are Poisson diffeomorphisms.
In this paper, the authors attempt to show that there is a geometric theory of Poisson fibrations that is analogous to the theory of symplectic fibrations. Their approach is based on gauge theory and Dirac geometry, and at the same time on integration of such structures, recovering symplectic fibrations from Poisson fibrations.
For the entire collection see [Zbl 1131.53002].

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
58H05 Pseudogroups and differentiable groupoids
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