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.
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.
@article{AIF_1992__42_4_967_0, author = {Xu, Ping}, 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}, zbl = {0759.58020}, mrnumber = {94d:58167}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1317/} }
TY - JOUR AU - Xu, Ping TI - Poisson cohomology of regular Poisson manifolds JO - Annales de l'Institut Fourier PY - 1992 SP - 967 EP - 988 VL - 42 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1317/ DO - 10.5802/aif.1317 LA - en ID - AIF_1992__42_4_967_0 ER -
Xu, Ping. Poisson cohomology of regular Poisson manifolds. Annales de l'Institut Fourier, Volume 42 (1992) no. 4, pp. 967-988. doi : 10.5802/aif.1317. https://aif.centre-mersenne.org/articles/10.5802/aif.1317/
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