arXiv subjects

Anne Thomas

Publications and source records attributed to Anne Thomas.

39 records · Page 3Linked to original sources

arXiv2007

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

math.GR↗

arXiv2006

A construction of lattices for certain hyperbolic buildings

We construct a nonuniform lattice and an infinite family of uniform lattices in the automorphism group of a hyperbolic building with all links a fixed finite building of rank 2 associated to a Chevalley group. We use complexes of groups and basic facts about spherical buildings.

math.GR↗

arXiv2005

Covolumes of uniform lattices acting on polyhedral complexes

Let X be a polyhedral complex with finitely many isometry classes of links. We establish a restriction on the covolumes of uniform lattices acting on X. When X is two-dimensional and has all links isometric to either a complete bipartite graph or the building for a Chevalley group of rank 2 over a field of prime order, we obtain further restrictions on covolumes.

math.GR↗