This article is cited in 5 papers

Global formality at the $G_\infty$-level

Damien Calaque^ab, Michel Van den Bergh<sup>c

a</sup> Université de Lyon, Université Lyon 1, Institut Camille Jordan CNRS UMR 5208, Villeurbanne Cedex
^b Department of Mathematics, ETH Zurich, Zurich, Switzerland
^c Departement WNI, Universiteit Hasselt, Diepenbeek, Belgium

Abstract: In this paper we prove that the sheaf of $\mathcal L$-polydifferential operators for a locally free Lie algebroid $\mathcal L$ is formal when viewed as a sheaf of $G_\infty$-algebras via Tamarkin's morphism of DG-operads $G_\infty\to B_\infty$.
In an appendix we prove a strengthening of Halbout's globalization result for Tamarkin's local quasi-isomorphism.

Key words and phrases: deformation quantization.

MSC: 14F99, 14D99

Received: September 30, 2008

Language: English

DOI: 10.17323/1609-4514-2010-10-1-31-64

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