Narrow Results

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.

We give a precise formulation of T-duality for Ramond–Ramond fields. This gives a canonical isomorphism between the "geometrically invariant" subgroups of the twisted differentialK-theory groups associated to certain principal torus bundles. Our result combines topological T-duality with the Buscher rules found in physics.