Gomi, K.Thiang, G.C.2019-06-102019-06-102019Journal of Geometry and Physics, 2019; 139:50-770393-04401879-1662http://hdl.handle.net/2440/119418We 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.en© 2019 Elsevier B.V. All rights reserved.T-duality; topological phases; crystallographyJournal article003010901510.1016/j.geomphys.2019.01.0020004628102000042-s2.0-85061278651430249Thiang, G.C. [0000-0003-0268-0065]