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Halbout, Gilles
Formality theorems : from associators to a global formulation. Annales mathématiques Blaise Pascal, 13 no. 2 (2006), p. 313-348
Texte intégral djvu | pdf | Analyses MR 2275450 | Zbl 05127367

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Résumé

Let $M$ be a differential manifold. Let $\Phi $ be a Drinfeld associator. In this paper we explain how to construct a global formality morphism starting from $\Phi $. More precisely, following Tamarkin’s proof, we construct a Lie homomorphism “up to homotopy” between the Lie algebra of Hochschild cochains on $C^{\infty }(M)$ and its cohomology $(\Gamma (M,\Lambda TM), ~[-,-]_S$). 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 $G_\infty $-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.

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