Preprint A429/2005
Poisson geometry and Morita equivalence
Alan Weinstein | Bursztyn, Henrique
Keywords: Poisson manifold | Picard group | Morita equivalence
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.