English

On \pi-surfaces of four-dimensional parallelohedra

Metric Geometry 2017-11-15 v1 Combinatorics

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 group of rational first homologies of its \pi-surface is generated by half-belt cycles.

Keywords

Cite

@article{arxiv.1309.7661,
  title  = {On \pi-surfaces of four-dimensional parallelohedra},
  author = {Alexey Garber},
  journal= {arXiv preprint arXiv:1309.7661},
  year   = {2017}
}

Comments

16 pages, 7 figures