Abstract
We show that every four-dimensional parallelohedron P satisfies a recently found condition of Garber, Gavrilyuk & Magazinov sufficient for the Voronoi conjecture being true for P. Namely, we show that for every four-dimensional parallelohedron P the one-dimensional homology group of its \({\pi}\)-surface is generated by half-belt cycles.
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Garber, A. On \({\pi}\)-Surfaces of Four-Dimensional Parallelohedra. Ann. Comb. 21, 551–572 (2017). https://doi.org/10.1007/s00026-017-0366-9
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DOI: https://doi.org/10.1007/s00026-017-0366-9