Leighton's Theorem and Regular Cube Complexes
Group Theory
2023-10-04 v2 Geometric Topology
Abstract
Leighton's graph covering theorem states that two finite graphs with common universal cover have a common finite cover. We generalize this to a large family of non-positively curved special cube complexes that form a natural generalization of regular graphs. This family includes both hyperbolic and non-hyperbolic CAT(0) cube complexes.
Cite
@article{arxiv.2109.03295,
title = {Leighton's Theorem and Regular Cube Complexes},
author = {Daniel J. Woodhouse},
journal= {arXiv preprint arXiv:2109.03295},
year = {2023}
}
Comments
17 pages, 3 figures, comments welcome The separable subgroup condition was not quite strong enough in the previous version and has been strengthened appropriately