Poisson geometry and Morita equivalence

Details Poisson geometry and Morita equivalence Poisson geometry and Morita equivalence

2004-02-22

arxiv.org/abs/math/0402347v2

Mathematics

Symplectic Geometry

52 pages. Expanded notes from the mini-course taught by A. Weinstein at the PQR 2003 Euroschool in Brussels. Revised version,

Scientific paper

These notes discuss various aspect of the ``representation theory'' of Poisson manifolds, with focus on Morita equivalence and Picard groups. We give a brief introduction to Poisson geometry (including Dirac and twisted Poisson structures) and algebraic Morita theory before presenting the geometric Morita theory of Poisson manifolds. We also point out the connections with the theory of symplectic groupoids and hamiltonian actions.

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