A classification of topologically stable Poisson structures on a compact oriented surface (Q2491042)

This paper concerns the global classification of Poisson structures on a given manifold. The Weinstein splitting theorem stipulates that the local classification of Poisson manifolds can be reduced to classification of structures vanishing at a point. In this work, the author studies the relation with the global classification. Actually, the author gives an explicit example of a global classification on a compact oriented surface. Applications for Poisson structures on the sphere are finally discussed.