no. 4
Poisson cohomology of regular Poisson manifolds
Annales de l'Institut Fourier, Tome 42 (1992) no. 4, pp. 967-988.

Le but principal de cet article est de proposer une méthode pour calculer la cohomologie de Poisson d’une variété de Poisson par l’utilisation de groupoïdes symplectiques.

L’idée clé est de se ramener à calculer la cohomologie de Rham de certaines variétés. En particulier nous en déduisons une formule pour la cohomologie de Poisson d’une variété de Poisson régulière dont la feuilletage symplectique est trivial.

The main purpose of this paper is to suggest a method of computing Poisson cohomology of a Poisson manifold by means of symplectic groupoids. The key idea is to convert the problem of computing Poisson cohomology to that of computing de Rham cohomology of certain manifolds. In particular, we shall derive an explicit formula for the Poisson cohomology of a regular Poisson manifold where the symplectic foliation is a trivial fibration.

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     title = {Poisson cohomology of regular {Poisson} manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {967--988},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {42},
     number = {4},
     year = {1992},
     doi = {10.5802/aif.1317},
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     zbl = {0759.58020},
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Xu, Ping. Poisson cohomology of regular Poisson manifolds. Annales de l'Institut Fourier, Tome 42 (1992) no. 4, pp. 967-988. doi : 10.5802/aif.1317. http://www.numdam.org/articles/10.5802/aif.1317/

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