On pi-Surfaces of Four-Dimensional Parallelohedra

摘要

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 -surface is generated by half-belt cycles.