Crystallographic T-duality
arXiv:1806.11385 · doi:10.1016/j.geomphys.2019.01.002
Abstract
We introduce the notion of crystallographic T-duality, inspired by the appearance of -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.
49 pages, 4 figures, 3 tables. Revised version with expanded appendix, for publication in J. Geom. Phys