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A classification of topologically stable Poisson structures on a compact oriented surface. (English) Zbl 1093.53087

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.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
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