Counting Overlattices for Polyhedral Complexes
نویسنده
چکیده
We investigate the asymptotics of the number of “overlattices” of a cocompact lattice Γ in Aut(X), where X is a locally finite polyhedral complex. We use complexes of groups to prove an upper bound for general X, and a lower bound for certain right-angled buildings.
منابع مشابه
Coverings of Complexes of Groups, with an Application to Counting Overlattices
We begin with some covering theory for complexes of groups. For example, we show that a covering of developable complexes of groups induces a monomorphism of fundamental groups, and an equivariant isometry of universal covers. As an application, we then investigate the asymptotics of the number of “overlattices” of a cocompact lattice Γ in Aut(K), where K is a locally finite polyhedral complex....
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