Crystallographic T-duality

Abstract

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.

arXiv comment49 pages, 4 figures, 3 tables. Revised version with expanded appendix, for publication in J. Geom. Phys

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Cited by in corpus (6)

• Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Twisted crystallograpic T-duality via the Baum--Connes isomorphism
• The Geometry of (non-Abelian) Landau levels
• Topological Spectral Bands with Frieze Groups
• Lieb-Schultz-Mattis Theorem and the Filling Constraint