no. 1
Cohomologie tangente et cup-produit pour la quantification de Kontsevich
Manchon, Dominique1 ; Torossian, Charles2
1 CNRS - UMR 6620 Université Blaise Pascal 24 avenue des Landais 63177 Aubière cedex France
2 CNRS - UMR 8553 Ecole Normale Supérieure 45 rue d’Ulm 75230 Paris Cedex 05 France
Annales mathématiques Blaise Pascal, Tome 10 (2003) no. 1, pp. 75-106.
corrigé par Erratum : Cohomologie tangente et cup-produit pour la quantification de Kontsevich

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

DOI : 10.5802/ambp.168
Manchon, Dominique 1 ; Torossian, Charles 2

1 CNRS - UMR 6620 Université Blaise Pascal 24 avenue des Landais 63177 Aubière cedex France
2 CNRS - UMR 8553 Ecole Normale Supérieure 45 rue d’Ulm 75230 Paris Cedex 05 France 
@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://archive.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://archive.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://archive.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, Tome 10 (2003) no. 1, pp. 75-106. doi : 10.5802/ambp.168. http://archive.numdam.org/articles/10.5802/ambp.168/

[1] Andler, M.; Dvorsky, A.; Sahi, S. Kontsevich quantization and invariant distributions on Lie groups, Ann. Sci. Ec.Normale Sup. (4), Volume 35, no.3  (2002), pp. 371-390 | Numdam | MR | Zbl

[2] Arnal, D.; Manchon, D.; Masmoudi, M. Choix des signes pour la formalité de Kontsevich, Pacific J. Math., Volume 203 (2002), pp. 23-66 | DOI | MR | Zbl

[3] Bayen, F.; Flato, M.; Frønsdal, C.; Lichnerowicz, A.; Sternheimer, D. Deformation theory and quantization I. Deformations of symplectic structures, Ann. Phys., Volume 111 (1978), pp. 61-110 | DOI | MR | Zbl

[4] Cattaneo, A.; Felder, G.; Tomassini, L. From local to global deformation quantization of Poisson manifolds (2000) (arXiv : math/QA/0012228) | Zbl

[5] Fulton, W.; MacPherson, R. Compactification of configuration spaces, Ann. Math., Volume 139 (1994), pp. 183-225 | DOI | MR | Zbl

[6] Ginot, G.; Halbout, G. A deformed version of Tamarkin’s formality theorem (2002) (Prépublication, IRMA Strasbourg)

[7] Kontsevich, M. Deformation quantization of Poisson manifolds I (1997) (arXiv : math/QA/9709040)

[8] Mochizuki, T. On the morphism of Duflo-Kirillov type, Journal of Geometry and Physics, Volume 41 (2002), pp. 73-113 | DOI | MR | Zbl

[9] Tamarkin, D. Another proof of M. Kontsevich Formality theorem for R-n (1998) (arXiv : math/QA/9803025)

Cité par Sources :