Special Symplectic Connections and Poisson Geometry |
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Authors: | Michel Cahen LORENZ J. SCHWACHHÖ FER |
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Affiliation: | (1) Université Libre de Bruxelles, Campus Plaine, Belgium;(2) Universität Dortmund, Vogelpothsweg 87, Germany |
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Abstract: | By a special symplectic connection we mean a torsion free connection which is either the Levi-Civita connection of a Bochner-Kähler metric of arbitrary signature, a Bochner-bi-Lagrangian connection, a connection of Ricci type or a connection with special symplectic holonomy. A manifold or orbifold with such a connection is called special symplectic. We show that any special symplectic connection can be constructed using symplectic realizations of quadratic deformations of a certain linear Poisson structure. Moreover, we show that these Poisson structures cannot be symplectically integrated by a Hausdorff groupoid. As a consequence, we obtain a canonical principal line bundle over any special symplectic manifold or orbifold, and we deduce numerous global consequences. |
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Keywords: | symplectic connections poisson manifolds symplectic groupoids |
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