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abstract: 'We construct a 2-colored operad ${{\bf Ger}}^+_{\infty}$ which, on the one hand, extends the operad ${{\bf Ger}}_{\infty}$ governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored operad governing open-closed homotopy algebras (OCHA). We show that Tamarkin’s ${{\bf Ger}}_{\infty}$-structure on the Hochschild cochain complex ${C^{\bullet}}(A,A)$ of an $A_{\infty}$-algebra $A$ extends naturally to a ${{\bf Ger}}^+_{\infty}$-structure on the pair $({C^{\bullet}}(A,A), A)$. We show that a formality quasi-isomorphism for the Hochschild cochains of the polynomial algebra can be obtained via transfer of this ${{\bf Ger}}^+_{\infty}$-structure to the cohomology of the pair $({C^{\bullet}}(A,A), A)$. We show that ${{\bf Ger}}^+_{\infty}$ is a sub DG operad of the first sheet $E^1({{\rm SC}})$ of the homology spectral sequence for the Fulton-MacPherson version ${{\rm SC}}$ of Voronov’s Swiss Cheese operad. Finally, we prove that the DG operads ${{\bf Ger}}^+_{\infty}$ and $E^1({{\rm SC}})$ are non-formal.'
author:
- Vasily Dolgushev
title: Formality theorem for Hochschild cochains via transfer
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[*Belatedly to Simon Lyakhovich on the occasion of his 50th birthday.*]{}

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[*Keywords:*]{} Operads, formality theorems, homotopy algebras.\
[*2010 MSC:*]{} 18D50, 55U35.

Introduction
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This paper is devoted to a natural $2$-colored extension ${{\bf Ger}}^+_{\infty}$ of the operad ${{\bf Ger}}_{\infty}$ governing homotopy Gerstenhaber algebras. Informally a 