abstract
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.
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