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Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: E2 pages for 1651 magnetic space groups

Ken Shiozaki1 and Seishiro Ono2,3

  • 1Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
  • 2Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
  • 3RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN, Wako 351-0198, Japan

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Phys. Rev. B 113, 195441 – Published 27 May, 2026

DOI: https://doi.org/10.1103/bvfl-ff5t

Abstract

We compute the E2 pages of the momentum-space and real-space Atiyah-Hirzebruch spectral sequence (AHSS) for topological crystalline insulators and superconductors up to three spatial dimensions, using cell decompositions such that any group element that fixes a cell setwise also fixes it pointwise. We provide a detailed description of the implementation for computing the E2 pages of AHSS. Under a physically reasonable assumption, we enumerate all possible K-groups that are compatible with the E2 pages for both momentum and real-space AHSS. As a result, we determined the K-groups for approximately 59% of symmetry settings in three spatial dimensions.

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Outline

Information

Phys. Rev. B 113, 195441– Published 27 May, 2026
  • Received 8 June 2023
  • Revised 25 March 2026
  • Accepted 14 April 2026
Article part of CHORUS
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