spectral sequence

Physical review. B./Physical review. B

We study the Atiyah-Hirzebruch spectral sequence (AHSS) for equivariant\nK-theory in the context of band theory. Various notions in the band theory such\nas irreducible representations at high-symmetric points, the compatibility\nrelation, topological gapless and singular points naturally fits into the AHSS.\nAs an application of the AHSS, we get the complete list of topological\ninvariants for 230 space groups without time-reversal or particle-hole\ninvariance. We find that a lot of torsion topological invariants appear even\nfor symmorphic space groups.\n

Atiyah-Hirzebruch spectral sequence in band topology: General formalism and topological invariants for 230 space groups