Résumé
Let$\g\_2$be the Hochschild 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 ( i.e. Gerstenhaber algebra up to homotopy structure) on$\g\_2$ , and any$C\_\infty$ -morphism$\phi$( i.e. morphism of commutative, associative 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$\phi$ . We also show that any$L\_\infty$ -morphism ( i.e. morphism of Lie algebra up to homotopy), in particular the one constructed by Kontsevich, can be deformed into a$G\_\infty$ -morphism, using Tamarkin's method for any$G\_\infty$ -structure on$\g\_2$ . We also show that any two of such$G\_\infty$ -morphisms are homotopic.