Upper-degree conjecture for generators and relations of 3D space-group cohomology

Let GG be a 3D space group and consider its mod-2 cohomology ring H(G,Z2)H^*(G,\mathbb{Z}_2). Upper-degree conjecture for generators and relations. An independent generator can appear at most in degree 66, and an independent relation can appear at most in degree 1212. 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.

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Primary source

Chunxiao Liu and Weicheng Ye, “Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints”, arXiv:2410.03607 (2026).

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