The mukai pairing - II: the Hochschild-Kostant-Rosenberg isomorphism

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 K-0(X) -> HH0(X) becomes, after the HKR isomorphism, the usual one K-0(X) -> circle plus H-i(X, Omega(I)(X)); and we present a conjecture that relates the Hochschild and harmonic structures of a smooth space, similar in spirit to the Tsygan formality conjecture. (c) 2004 Elsevier Inc. All rights reserved.