Formality of cyclic cochains (Q452038)

This paper proves a conjecture of M. Kontsevich about cyclic formality. Let us recall that M. Kontsevich has proved a famous formality theorem which stipulates the existence of a star product on any Poisson manifold. In this work, the authors concentrate on the cyclic analog. They prove that the differential graded Lie algebra of polydifferential cyclic cochains of the algebra of smooth functions on a manifold is L-infty-quasi-isomorphic to the second term in the spectral sequence. This result enables the authors to obtain a full classification of all closed star products.