The Mukai pairing, II: the Hochschild-Kostant-Rosenberg isomorphism
Andrei Caldararu
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 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) Hi(X, ΩXi); and -- we present a conjecture that relates the Hochschild and harmonic structures of a smooth space.
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