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 Mukai pairing on differential forms that applies to arbitrary manifolds; -- we give a proof of the fact that the natural Chern character map $K_0(X)\to H{H}_0(X)$ becomes, after the HKR isomorphism, the usual one $K_0(X)\to ⨁H^i(X,{\Omega }_X^i)$; and -- we present a conjecture that relates the Hochschild and harmonic structures of a smooth space.

19 pages, uses diagrams.sty, corrected proofs of Theorems 4.1 and 4.4 following a suggestion of Amnon Yekutieli

References in corpus (3)

• A New Cohomology Theory for Orbifold
• The Mukai pairing, I: the Hochschild structure
• Tsygan formality and Duflo formula

Cited by in corpus (6)

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• Lectures on Noncommutative Geometry
• Multiplicative structure on the Hochschild cohomology of crossed product algebras
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• Line bundle twisted chiral de Rham complex and bound states of D-branes on toric manifolds