Cohomologie tangente et cup-produit pour la quantification de Kontsevich
Dominique Manchon, Charles Torossian
Abstract
On a flat manifold, M. Kontsevich's formality quasi-isomorphism is compatible with cup-products on tangent cohomology spaces, in the sense that its derivative at any formal Poisson 2-tensor induces an isomorphism of graded commutative algebras from Poisson cohomology space to Hochschild cohomology space relative to the associated deformed multiplication. We give here a detailed proof of this result, with signs and orientations precised.
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