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.

中文翻译：

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通过 Baum-Connes 同构的扭曲晶体学 T 对偶

我们建立了扭曲晶体学 T 对偶，这是与晶体学群的扩展相关的位置和动量环的 Freed-Moore 扭曲等变 K 群之间的同构。证明是通过用扭曲的 Chabert-Echterhoff KK 理论中的 Dirac 同态来识别映射来给出的。我们还说明了如何在 K 理论计算中利用它。