Leighton's Theorem and Regular Cube Complexes
arXiv:2109.03295 · doi:10.2140/agt.2023.23.3395
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.
17 pages, 3 figures, comments welcome The separable subgroup condition was not quite strong enough in the previous version and has been strengthened appropriately