11,815 research outputs found
Coverings by open cells
We prove that in a semi-bounded o-minimal expansion of an ordered group every
non-empty open definable set is a finite union of open cells.Comment: 17 pages, revised versio
Covering theory for complexes of groups
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 in the
automorphism group of a locally finite polyhedral complex .Comment: 47 pages, 1 figure. Comprises Sections 1-4 of previous submission.
New introduction. To appear in J. Pure Appl. Algebr
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