The Mukai pairing, I: the Hochschild structure
摘要
We study the Hochschild structure of a smooth space or orbifold, emphasizing the importance of a pairing defined on Hochschild homology which generalizes a similar pairing introduced by Mukai on the cohomology of a K3 surface. We discuss those properties of the structure which can be derived without appealing to the Hochschild-Kostant-Rosenberg isomorphism and Kontsevich formality, namely: -- functoriality of homology, commutation of push-forward with the Chern character, and adjointness with respect to the generalized pairing; -- formal Hirzebruch-Riemann-Roch and the Cardy condition from physics; -- invariance of the full Hochschild structure under Fourier-Mukai transforms. Connections with homotopy theory and TQFT's are discussed in an appendix. A separate paper treats consequences of the HKR isomorphism. Applications of these results to the study of a mirror symmetric analogue of Chen-Ruan's orbifold product will be presented in a future paper.
引用
@article{arxiv.math/0308079,
title = {The Mukai pairing, I: the Hochschild structure},
author = {Andrei Caldararu},
journal= {arXiv preprint arXiv:math/0308079},
year = {2016}
}
备注
32 pages, 3 figures,uses diagrams.sty; major revision, including improved definition of Chern character, connections with TQFT's, added references