Upper-degree conjecture for generators and relations of 3D space-group cohomology
Upper-degree conjecture for generators and relations of 3D space-group cohomology
Let be a 3D space group and consider its mod-2 cohomology ring . Upper-degree conjecture for generators and relations. An independent generator can appear at most in degree , and an independent relation can appear at most in degree . This conjecture would give a finite bound for computing presentations of the mod-2 cohomology rings of 3D space groups; the stated bounds are motivated by computations and by the structure of the Lyndon–Hochschild–Serre spectral sequence, but are not established in general.
Sources & referencesView supporting material
Primary source
Chunxiao Liu and Weicheng Ye, “Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints”, arXiv:2410.03607 (2026).
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