Radko, Olga A classification of topologically stable Poisson structures on a compact oriented surface. (English) Zbl 1093.53087 J. Symplectic Geom. 1, No. 3, 523-542 (2002). 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. Reviewer: Angela Gammella (Creil) Cited in 1 ReviewCited in 28 Documents MSC: 53D17 Poisson manifolds; Poisson groupoids and algebroids 53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) Keywords:Poisson manifolds; local and global classification PDFBibTeX XMLCite \textit{O. Radko}, J. Symplectic Geom. 1, No. 3, 523--542 (2002; Zbl 1093.53087) Full Text: DOI arXiv