Global formality at the $G_\infty$-level

TL;DR

This paper proves the formality of the sheaf of poly-differential operators associated with a Lie algebroid at the $G_infty$-level, extending Tamarkin's morphism and strengthening globalization results.

Contribution

It establishes the formality of the sheaf of poly-differential operators for Lie algebroids at the $G_infty$-level, using Tamarkin's morphism and improving existing globalization theorems.

Findings

Sheaf of poly-differential operators is formal as a $G_infty$-algebra.

Strengthened globalization result for Tamarkin's local quasi-isomorphism.

Extension of formality results to Lie algebroids.

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 $G_\infty\r B_\infty$. In an appendix we prove a strengthening of Halbout's globalization result for Tamarkin's local quasi-isomorphism.