Covering theory for complexes of groups

Details Covering theory for complexes of groups Covering theory for complexes of groups

2006-05-11

arxiv.org/abs/math/0605303v2

Mathematics

Group Theory

47 pages, 1 figure. Comprises Sections 1-4 of previous submission. New introduction. To appear in J. Pure Appl. Algebra

Scientific paper

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 $\Gamma$ in the automorphism group of a locally finite polyhedral complex $X$.

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