Poisson manifold

Summary

A Poisson manifold is a smooth manifold with a bracket on its smooth functions. The bracket has the algebraic properties of the Poisson bracket of a symplectic manifold. Every symplectic manifold is a Poisson manifold, but the bracket of a Poisson manifold may be degenerate. Poisson manifolds are the phase spaces of mechanics with constraints or symmetry, and they are the classical limits that deformation quantization starts from.