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Formality theorems: from associators to a global formulation

Gilles Halbout — 2006

Annales mathématiques Blaise Pascal

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 , Λ T M ) , [ - , - ] 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...

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