The Mukai pairing, II: the Hochschild-Kostant-Rosenberg isomorphism

الأصل · EN

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.