The Mukai pairing—II: the Hochschild–Kostant–Rosenberg isomorphism

Abstract: We continue the study of the Hochschild structure of a smooth space that we began in our previous paper, examining implications of the Hochschild–Kostant–Rosenberg theorem. The main contributions of the present paper are:[] we introduce a generalization of the usual notions of Mukai vector and Mukai pairing on differential forms that applies to arbitrary manifolds; [] we give a proof of the fact that the natural Chern character map becomes, after the HKR isomorphism, the usual one ; and [] we present a conjecture that relates the Hochschild and harmonic structures of a smooth space, similar in spirit to the Tsygan formality conjecture. [Copyright &y& Elsevier]