Formality theorems: from associators to a global formulation
Halbout, Gilles
Annales mathématiques Blaise Pascal, Tome 13 (2006), p. 313-348 / Harvested from Numdam
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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.

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     author = {Halbout, Gilles},
     title = {Formality theorems: from associators to a global formulation},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {13},
     year = {2006},
     pages = {313-348},
     doi = {10.5802/ambp.220},
     zbl = {1112.53067},
     mrnumber = {2275450},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2006__13_2_313_0}
}

Halbout, Gilles. Formality theorems: from associators to a global formulation. Annales mathématiques Blaise Pascal, Tome 13 (2006) pp. 313-348. doi : 10.5802/ambp.220. http://gdmltest.u-ga.fr/item/AMBP_2006__13_2_313_0/

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