no. 2
Formality theorems: from associators to a global formulation
Gilles Halbout1
1Institut 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 
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
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