Twisted crystallograpic T-duality via the Baum--Connes isomorphism

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.

65 pages. Minor revisions. Final version to appear in Int. J. Math