On a flat manifold , M. Kontsevich’s formality quasi-isomorphism is compatible with cup-products on tangent cohomology spaces, in the sense that for any formal Poisson -tensor the derivative at 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 via the quasi-isomorphism. We give here a detailed proof of this result, with signs and orientations precised.
@article{AMBP_2003__10_1_75_0, author = {Manchon, Dominique and Torossian, Charles}, title = {Cohomologie tangente et cup-produit pour la quantification de {Kontsevich}}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {75--106}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {10}, number = {1}, year = {2003}, doi = {10.5802/ambp.168}, zbl = {02068411}, mrnumber = {1990011}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/ambp.168/} }
TY - JOUR AU - Manchon, Dominique AU - Torossian, Charles TI - Cohomologie tangente et cup-produit pour la quantification de Kontsevich JO - Annales mathématiques Blaise Pascal PY - 2003 SP - 75 EP - 106 VL - 10 IS - 1 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.168/ DO - 10.5802/ambp.168 LA - fr ID - AMBP_2003__10_1_75_0 ER -
%0 Journal Article %A Manchon, Dominique %A Torossian, Charles %T Cohomologie tangente et cup-produit pour la quantification de Kontsevich %J Annales mathématiques Blaise Pascal %D 2003 %P 75-106 %V 10 %N 1 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.168/ %R 10.5802/ambp.168 %G fr %F AMBP_2003__10_1_75_0
Manchon, Dominique; Torossian, Charles. Cohomologie tangente et cup-produit pour la quantification de Kontsevich. Annales mathématiques Blaise Pascal, Volume 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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