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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 hγ the derivative at hγ 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 hγ via the quasi-isomorphism. We give here a detailed proof of this result, with signs and orientations precised.

Cohomologie tangente et cup-produit pour la quantification de Kontsevich