The Mukai pairing, II: the Hochschild-Kostant-Rosenberg isomorphism
By Andrei Căldăraru. 2003
187 citations recorded by the source corpus.
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 $K_0(X) \to HH_0(X)$ becomes, after the HKR isomorphism, the usual one $K_0(X) \to \bigoplus H^i(X, \Omega_X^i)$; and -- we present a conjecture that relates the Hochschild and harmonic structures of a smooth space.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c0d9ab7a7733c4ca1de71c25ecb5b55ea8cbd365
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- D. Shklyarov
- Simon Willerton
- N. Markarian
- L. Hille
- Michel van den Bergh
- Andrei Căldăraru
- Yukinobu Toda
- Bertrand Toën
In Mathematical Physics
- D. Shklyarov
- Simon Willerton
- N. Markarian
- L. Hille
- Michel van den Bergh
- Andrei Căldăraru
- Yukinobu Toda
- Bertrand Toën
Citations in the corpus
- The Mukai pairing, I: a categorical approach (2007, methodology): “SW has been supported by a WUN travel bursary and a Royal Society Conference grant.”
- Hodge theory and derived categories of cubic fourfolds (2012, unknown): “Secondly, in this low degree, the map ◦ exp( At S ) of [12, 17] reduces to Similarly, the image of in Ext 2 ( P, P ).”
- Handbook of Tilting Theory: Fourier-Mukai transforms (2004, methodology): “a [40] who proves the analogue of Theorem 3.2 for orbifolds. The real significance of Theorem 3.2 is that it makes it possible to define Φ on objects functorially derived from X and Y. For example (see [22, 59]) let ch′ X(−) = chX(−).Td(X)1/2 (where chX(−) is the Chern character and Td(X) is the Todd ”
- Hirzebruch–Riemann–Roch‐type formula for DG algebras (2007, background): “A new proof was obtained in [33, 34] using an algebraic-differential calculus (see also [10, 41]).”