Annales Mathématiques
Blaise Pascal
no. 2
Formality theorems: from associators to a global formulation
Gilles Halbout1
1 Institut de Recherche Mathématique Avancée Université Louis Pasteur 7, rue René Descartes 67084 Strasbourg Cedex FRANCE
Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 2, pp. 313-348.

Let M be a differential manifold. Let Φ be a Drinfeld associator. In this paper we explain how to construct a global formality morphism starting from Φ. More precisely, following Tamarkin’s proof, we construct a Lie homomorphism “up to homotopy" between the Lie algebra of Hochschild cochains on C ∞ (M) and its cohomology (Γ(M,ΛTM),[-,-] 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 ∞ -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.

DOI : 10.5802/ambp.220

Gilles Halbout 1

1 Institut de Recherche Mathématique Avancée Université Louis Pasteur 7, rue René Descartes 67084 Strasbourg Cedex FRANCE 
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Gilles Halbout. Formality theorems: from associators to a global formulation. Annales mathématiques Blaise Pascal, Tome 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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