Let $M$ be a differential manifold. Let $\Phi$ be a Drinfeld associator. In this paper we explain how to construct a global formality morphism starting from $\Phi$. More precisely, following Tamarkin’s proof, we construct a Lie homomorphism “up to homotopy" between the Lie algebra of Hochschild cochains on $C^{\infty }\left(M\right)$ and its cohomology $(\Gamma (M,\Lambda TM),{[-,-]}_S$). This paper is an extended version of a course given 8 - 12 March 2004 on Tamarkin’s works. The reader will find explicit examples, recollections on $G_{\infty }$-structures, explanation of the...

Dans cet article on donne une formule explicite pour le caractère de Chern reliant la $K$- théorie algébrique et l’homologie cyclique négative. On calcule le caractère de Chern des symboles de Steinberg et de Loday et on donne une preuve élémentaire du fait que le caractère de Chern est multiplicatif.

Constructing an even Poisson algebra from a Gerstenhaber algebra by means of an odd derivation of square 0 is shown to be possible in the category of Loday algebras (algebras with a non-skew-symmetric bracket, generalizing the Lie algebras, heretofore called Leibniz algebras in the literature). Such “derived brackets” give rise to Lie brackets on certain quotient spaces, and also on certain Abelian subalgebras. The construction of these derived brackets explains the origin of the Lie bracket on...