Topics of Symplectic Geometry (Poisson Geometry)

Poisson brackets and bivectors. Examples.

Local structure: Weinstein’s splitting, Transversal structure, Linearization problem.

Symplectic foliation.

Poisson invariants: cohomology, modular class.

Symplectic realization: Libermann’s theorem and dual pairs.

Symplectic groupoids: Integrability problem.

Poisson Lie groups and bialgebras.

Elements of Dirac geometry: pullbacks, pushforwards, gauge equivalences.

Submanifolds in Poisson geometry.

Reference:
M. Crainic, R. Fernandes, I. Marcut: Lectures on Poisson geometry. GMS 217, AMS.