Cohomologie tangente et cup-produit pour la quantification de Kontsevich

摘要

On a flat manifold $M=mathbb{R}^d$, 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 $hbargamma $ the derivative at $hbargamma $ 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 $hbargamma $ via the quasi-isomorphism. We give here a detailed proof of this result, with signs and orientations precised.