We develop an explicit covering theory for complexes of groups, parallel to that developed for graphs of groups by Bass. Given a covering of developable complexes of groups, we construct the induced monomorphism of fundamental groups and isometry of universal covers. We characterize faithful complexes of groups and prove a conjugacy theorem for groups acting freely on polyhedral complexes. We also define an equivalence relation on coverings of complexes of groups, which allows us to construct a bijection between such equivalence classes, and subgroups or overgroups of a fixed lattice Γ in the automorphism group of a locally finite polyhedral complex X. © 2007 Elsevier Ltd. All rights reserved.
Lim, S., & Thomas, A. (2008). Covering theory for complexes of groups. Journal of Pure and Applied Algebra, 212(7), 1632–1663. https://doi.org/10.1016/j.jpaa.2007.10.012