Global formality at the $G_{\infty }$-level

Abstract

In this paper we prove that the sheaf of $\Lscr$-poly-differential operators for a locally free Lie algebroid $\Lscr$ is formal when viewed as a sheaf of $G_{\infty }$-algebras via Tamarkin's morphism of DG-operads $G_{\infty }{\mathring{B}}_{\infty }$. In an appendix we prove a strengthening of Halbout's globalization result for Tamarkin's local quasi-isomorphism.

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