Covering theory for complexes of groups

• Autores: Seonhee Lim, Anne Thomas
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 7, 2008, págs. 1632-1663
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2007.10.012
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• Resumen

  • 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 G in the automorphism group of a locally finite polyhedral complex X.