On the existence of symplectic realizations (Q428968)

Let \((M,\pi )\) be a Poisson manifold. A symplectic realization of \((M,\pi )\) is a symplectic manifold \((S,\omega )\) together with a Poisson submersion \(\mu :(S,\omega )\rightarrow (M,\pi )\). In this paper the authors give a new proof of the existence of symplectic realizations of a Poisson manifold. The proof consists in the construction of a symplectic form on an open neighborhood of the zero-section of the cotangent bundle \(T^{*}M\), defined by an explicit global formula.