no. 1
Cohomologie tangente et cup-produit pour la quantification de Kontsevich
Manchon, Dominique1 ; Torossian, Charles2
1 CNRS - UMR 6620 Université Blaise Pascal 24 avenue des Landais 63177 Aubière cedex France
2 CNRS - UMR 8553 Ecole Normale Supérieure 45 rue d’Ulm 75230 Paris Cedex 05 France
Annales mathématiques Blaise Pascal, Tome 10 (2003) no. 1, pp. 75-106.
corrigé par Erratum : Cohomologie tangente et cup-produit pour la quantification de Kontsevich

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.

DOI : 10.5802/ambp.168
Manchon, Dominique 1 ; Torossian, Charles 2

1 CNRS - UMR 6620 Université Blaise Pascal 24 avenue des Landais 63177 Aubière cedex France
2 CNRS - UMR 8553 Ecole Normale Supérieure 45 rue d’Ulm 75230 Paris Cedex 05 France 
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Manchon, Dominique; Torossian, Charles. Cohomologie tangente et cup-produit pour la quantification de Kontsevich. Annales mathématiques Blaise Pascal, Tome 10 (2003) no. 1, pp. 75-106. doi : 10.5802/ambp.168. http://www.numdam.org/articles/10.5802/ambp.168/

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