abstract:In mathematics, a Poisson manifold is a smooth manifold M equipped with a bilinear map {⋅,⋅}M (called a Poisson bracket) on the algebra C∞(M) of smooth functions on M such that (C∞(M),{⋅,⋅}M) is a Poisson algebra. One usually denotes a Poisson manifold by the ordered pair (M,{⋅,⋅}M).