Twisted crystallograpic T-duality via the Baum--Connes isomorphism
K-Theory and Homology
2021-10-12 v2 Mathematical Physics
math.MP
Abstract
We establish the twisted crystallographic T-duality, which is an isomorphism between Freed-Moore twisted equivariant K-groups of the position and momentum tori associated to an extension of a crystallographic group. The proof is given by identifying the map with the Dirac homomorphism in twisted Chabert--Echterhoff KK-theory. We also illustrate how to exploit it in K-theory computations.
Cite
@article{arxiv.2102.00393,
title = {Twisted crystallograpic T-duality via the Baum--Connes isomorphism},
author = {Kiyonori Gomi and Yosuke Kubota and Guo Chuan Thiang},
journal= {arXiv preprint arXiv:2102.00393},
year = {2021}
}
Comments
65 pages. Minor revisions. Final version to appear in Int. J. Math