On the K-theory classification of topological phases of matter for the case of topological crystalline insulators classified by equivariant K-theory:
Jorrit Kruthoff, Jan de Boer, Jasper van Wezel, Charles L. Kane, Robert-Jan Slager, Topological Classification of Crystalline Insulators through Band Structure Combinatorics, Phys. Rev. X 7 (2017) 041069 $[$doi:10.1103/PhysRevX.7.041069$]$
Luuk Stehouwer, Jan de Boer, Jorrit Kruthoff, Hessel Posthuma, Classification of crystalline topological insulators through K-theory, Adv. Theor. Math. Phys, 25 3 (2021) 723–775 [arXiv:1811.02592, doi:10.4310/ATMP.2021.v25.n3.a3]
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