| Résume||According to Hochschild-Kostant-Rosenberg theorem,
for a smooth manifold $M$, the Hochschild cohomology of the
algebra of smooth functions $C^\infty (M)$ (with values in itself)
is naturally isomorphic, via the HKR-map, to the space of polyvector fields
on $M$ as Gerstenhaber algebras.
In this talk, we will discuss how to extend
this theorem to the situation when $M$ is replaced by
the leaf space of a foliation. In this case, a correction term--- the
square root of the Todd class of the foliation is needed.
The talk is based on the joint works with Z. Chen, H.-Y. Liao, M. Stienon and M. Xiang.|