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Crystallographic T-duality. (English) Zbl 1439.19010
Summary: We introduce the notion of crystallographic T-duality, inspired by the appearance of \(K\)-theory with graded equivariant twists in the study of topological crystalline materials. Besides giving a range of new topological T-dualities, it also unifies many previously known dualities, motivates generalisations of the Baum-Connes conjecture to graded groups, provides a powerful tool for computing topological phase classification groups, and facilitates the understanding of crystallographic bulk-boundary correspondences in physics.

MSC:
19L50 Twisted \(K\)-theory; differential \(K\)-theory
20H15 Other geometric groups, including crystallographic groups
81P94 Quantum cryptography (quantum-theoretic aspects)
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