Cohomologie tangente et cup-produit pour la quantification de Kontsevich
Manchon, Dominique ; Torossian, Charles
Annales mathématiques Blaise Pascal, Tome 10 (2003), p. 75-106 / Harvested from Numdam
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On a flat manifold M=ℝ d , M. Kontsevich’s formality quasi-isomorphism is compatible with cup-products on tangent cohomology spaces, in the sense that for any formal Poisson 2-tensor ℏγ the derivative at ℏγ of the quasi-isomorphism induces an isomorphism of graded commutative algebras from Poisson cohomology space to Hochschild cohomology space relative to the deformed multiplication built from ℏγ via the quasi-isomorphism. We give here a detailed proof of this result, with signs and orientations precised.

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     author = {Manchon, Dominique and Torossian, Charles},
     title = {Cohomologie tangente et cup-produit pour la quantification de Kontsevich},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {10},
     year = {2003},
     pages = {75-106},
     doi = {10.5802/ambp.168},
     zbl = {02068411},
     mrnumber = {1990011},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AMBP_2003__10_1_75_0}
}

Manchon, Dominique; Torossian, Charles. Cohomologie tangente et cup-produit pour la quantification de Kontsevich. Annales mathématiques Blaise Pascal, Tome 10 (2003) pp. 75-106. doi : 10.5802/ambp.168. http://gdmltest.u-ga.fr/item/AMBP_2003__10_1_75_0/

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