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Blaise Pascal
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Dominique Manchon; Charles Torossian
Cohomologie tangente et cup-produit pour la quantification de Kontsevich
Annales mathématiques Blaise Pascal, 10 no. 1 (2003), p. 75-106, doi: 10.5802/ambp.168
Article PDF | Reviews MR 1990011 | Zbl 02068411
See also an erratum to this article

Résumé - Abstract

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

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