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Twisted crystallograpic T-duality via the Baum--Connes isomorphism (2102.00393v2)
Published 31 Jan 2021 in math.KT, math-ph, and 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.