 

Andrei Căldăraru and Simon Willerton
The Mukai pairing. I. A categorical approach view print


Published: 
May 21, 2010 
Keywords: 
Hochschild homology, Mukai pairing, twocategory of varieties, Cardy condition, integral kernel, FourierMukai transform 
Subject: 
18E30 (primary), 14F05, 81T45 


Abstract
We study the Hochschild homology of smooth spaces, emphasizing the
importance of a pairing which generalizes Mukai's pairing on the
cohomology of K3 surfaces. We show that integral transforms between
derived categories of spaces functorially induce linear maps on
homology. Adjoint functors induce adjoint linear maps with respect
to the Mukai pairing. We define a Chern character with values in
Hochschild homology, and we discuss analogues of the
HirzebruchRiemannRoch theorem and the Cardy Condition from
physics. This is done in the context of a 2category which has
spaces as its objects and integral kernels as its 1morphisms.


Acknowledgements
AC's initial work on this project was supported by an NSF postdoctoral fellowship, and by travel grants and hospitality from the University of Pennsylvania, the University of Salamanca, Spain, and the Newton Institute in Cambridge, England. AC's current work is supported by the National Science Foundation under Grant No. DMS0556042. SW has been supported by a WUN travel bursary and a Royal Society Conference grant.


Author information
Andrei Căldăraru:
Mathematics Department, University of WisconsinMadison, 480 Lincoln Drive, Madison, WI 537061388, USA
andreic@math.wisc.edu
Simon Willerton:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK
S.Willerton@sheffield.ac.uk

