THE MUKAI PAIRING, II: THE HOCHSCHILD-KOSTANT-ROSENBERG ISOMORPHISM

Abstract

Abstract. We continue the study of the Hochschild structure of a smooth space that we began in [7], examining implications of the Hochschild-Kostant-Rosenberg theorem. The main contributions of the present paper are: – we introduce a generalization of the usual Mukai pairing on differential forms that applies to arbitrary manifolds; – we give a proof of the fact that the natural Chern character map K0(X)→HH0(X) becomes, after the HKR isomorphism, the usual one K0(X) → ⊕ H i (X,Ω i X); and – we present a conjecture that relates the Hochschild and harmonic structures of a smooth space. 1.