# Lifts of $L_\infty$-morphims to $G_\infty$-morphisms

Abstract : Let $\g_2$ be theHochschild complex of cochains on $C^\infty(\RM^n)$ and $\g_1$ be the space of multivector fields on $\RM^n$.In this paper we prove that given any $G_\infty$-structure ({\rm i.e.}Gerstenhaber algebra up to homotopy structure) on $\g_2$,and any morphism $\varphi$ of Lie algebra up to homotopy between$\g_1$ and $\g_2$, there exists a $G_\infty$-morphism $\Phi$between$\g_1$ and $\g_2$ that restricts to $\varphi$. In particular, themorphism constructed by Kontsevich can be obtained using Tamarkin'smethod for any $G_\infty$-structure on $\g_2$. We also show thatany two of such $G_\infty$-morphisms are homotopic in a certain sense.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00000272
Contributor : Grégory Ginot <>
Submitted on : Tuesday, April 1, 2003 - 9:08:39 AM
Last modification on : Thursday, January 11, 2018 - 6:12:22 AM
Long-term archiving on : Monday, March 29, 2010 - 3:38:28 PM

### Citation

Grégory Ginot, Gilles Halbout. Lifts of $L_\infty$-morphims to $G_\infty$-morphisms. 2003. ⟨hal-00000272v1⟩

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