Let be a differential manifold. Let be a Drinfeld associator. In this paper we explain how to construct a global formality morphism starting from . More precisely, following Tamarkin’s proof, we construct a Lie homomorphism “up to homotopy" between the Lie algebra of Hochschild cochains on and its cohomology ). This paper is an extended version of a course given 8 - 12 March 2004 on Tamarkin’s works. The reader will find explicit examples, recollections on -structures, explanation of the Etingof-Kazhdan quantization-dequantization theorem, of Tamarkin’s cohomological obstruction and of globalization process needed to get the formality theorem. Finally, we prove here that Tamarkin’s formality maps can be globalized.
@article{AMBP_2006__13_2_313_0, author = {Gilles Halbout}, title = {Formality theorems: from associators to a global formulation}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {313--348}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {13}, number = {2}, year = {2006}, doi = {10.5802/ambp.220}, mrnumber = {2275450}, zbl = {1112.53067}, language = {en}, url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.220/} }
TY - JOUR AU - Gilles Halbout TI - Formality theorems: from associators to a global formulation JO - Annales mathématiques Blaise Pascal PY - 2006 SP - 313 EP - 348 VL - 13 IS - 2 PB - Annales mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.220/ DO - 10.5802/ambp.220 LA - en ID - AMBP_2006__13_2_313_0 ER -
%0 Journal Article %A Gilles Halbout %T Formality theorems: from associators to a global formulation %J Annales mathématiques Blaise Pascal %D 2006 %P 313-348 %V 13 %N 2 %I Annales mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.220/ %R 10.5802/ambp.220 %G en %F AMBP_2006__13_2_313_0
Gilles Halbout. Formality theorems: from associators to a global formulation. Annales mathématiques Blaise Pascal, Volume 13 (2006) no. 2, pp. 313-348. doi : 10.5802/ambp.220. https://ambp.centre-mersenne.org/articles/10.5802/ambp.220/
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