Lectures on the Geometry of Poisson Manifolds

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This text aims to provide readers with a monograph that enables them to study systematically basic and advanced material on the recently developed theory of Poisson manifolds, and that also offers ready access to bibliographical references for the continuation of their study. The main subjects treated are: the Schouten-Nijenhuis bracket; the generalized Frobenius theorem; the basics of Poisson manifolds; Poisson calculus and cohomology; quantization; Poisson morphisms and reduction; and realizations of Poisson manifolds by symplectic manifolds and by symplectic groupoids and Poisson-Lie groups. The book unifies terminology and notation. It also reports on some original developments stemming from the author’s work, including new results on Poisson cohomology and geometric quantization, cofoliations and bi-invariant Poisson structures on Lie groups. The book is addressed to graduate students and researchers in the fields of mathematics and physics who are interested in mathematical and theoretical physics, differential geometry, mechanics, quantization theories and quantum physics, quantum groups and so on, and who are familiar with differntiable and symplectic manifolds.