Classification of topological insulators and superconductors is manifested in terms of spin cobordism groups for lower dimensions. It is discussed that the periodic table of topological insulators is a result of the possible choices of spin structures on Brillouin zones of relevant topological materials. This framework is extended to the case of Weyl semimetals. It is shown that the classification of Weyl semimetals can be managed in terms of spin$^c$ cobordism groups via the extension of spin structures to spin$^c$ structures. Topological invariants of Weyl semimetals are connected to the topological invariants of spin$^c$ cobordism groups and Fermi arcs of Weyl semimetals are interpreted in terms of the choices of spin$^c$ structures.
Symmetries, Dimensions, and Topological Insulators: the mechanism behind the face of the Bott clock
Periodic table for topological insulators and superconductors
Electric-Magnetic Duality and Topological Insulators
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