Baum-Connes and the Fourier-Mukai transform
K-Theory and Homology
2020-07-29 v2 Operator Algebras
Abstract
The Baum-Connes map for finitely generated free abelian groups is a K-theoretic analogue of the Fourier-Mukai transform from algebraic geometry. We describe this K-theoretic transform in the language of topological correspondences, and compute its action on K-theory (of tori) described geometrically in terms of Baum-Douglas cocycles, showing that the Fourier-Mukai transform maps the class of a subtorus to the class of a suitably defined dual torus. We deduce the Fourier-Mukai inversion formula. We use these results to give a purely geometric description of the Baum-Connes assembly map for free abelian groups.
Cite
@article{arxiv.2001.06124,
title = {Baum-Connes and the Fourier-Mukai transform},
author = {Heath Emerson and Dan Hudson},
journal= {arXiv preprint arXiv:2001.06124},
year = {2020}
}
Comments
Re-written and re-titled from the first version