Geodesic
Quantum de Rham cohomology ring for Poisson manifolds
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 192-196 
V. V. Shurygin (Jr.). Quantum de Rham cohomology ring for Poisson manifolds. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 192-196. http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a18/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In [4] we have proved that the quantum de Rham cohomology of a Poisson manifold $(M, \omega)$ (see [1]) can be obtained via deformational quantization of the de Rham cohomology of $M$. In this paper we prove that the ring structure on the quantum cohomology of $(M,\omega)$ is obtained via deformational quantization of the ring structure of de Rham cohomology of $M$.

[1] Cao H.-D., Zhou J., On quantum de Rham cohomology, Preprint math.DG/9806157, 1998

[2] Koszul J.-L., “Crochet de Schouten-Nijenhuis et cohomologie”, The mathematical heritage of Élie Cartan (Lyon, 1984), Astérisque, 1985, Numero Hors Serie, 257–271 | MR | Zbl

[3] A. Lichnerowicz, “Les variétés de Poisson et leurs algèbres de Lie associées”, J. Diff. Geom., 12 (1977), 253–300 | MR | Zbl

[4] Shurygin V. V.(ml.), “Kogomologii dvoinogo kompleksa Brylinskogo puassonovykh mnogoobrazii i kvantovye kogomologii de Rama”, Izv. vuzov. Matematika, 2004, no. 10, 75–81 | MR | Zbl