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Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints
We present a computational study of the mod-2 cohomology of three-dimensional (3D) space groups, with an eye toward their applications in Lieb--Schultz--Mattis constraints. We prove finite-generation results for the cohomology of crystallographic groups and give ring presentations for $H^*(G,\mathbb
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