Hochschild Cohomology of dg Manifolds Associated to Integrable Distributions

For the field K= R or C, and an integrable distribution F⊆ T_M⊗ _RK on a smooth manifold M, we study the Hochschild cohomology of the dg manifold (F[1] , d_F) and establish a canonical isomorphism with the Hochschild cohomology of the algebra of functions on leaf space in terms of transversal polydifferential operators of F. In particular, for the dg manifold (TX0,1[1],∂¯) associated with a complex manifold X, we prove that its Hochschild cohomology is canonically isomorphic to the Hochschild cohomology HH∙(X) of the complex manifold X. As an application, we show that the Duflo-Kontsevich type theorem for the dg manifold (TX0,1[1],∂¯) implies the Duflo-Kontsevich theorem for complex manifolds.