210 research outputs found
A family of uniform lattices acting on a Davis complex with a non-discrete set of covolumes
Let be a Coxeter system with Davis complex . The polyhedral
automorphism group of is a locally compact group under the
compact-open topology. If is a discrete group (as characterised by
Haglund--Paulin), then the set of uniform lattices in is
discrete. Whether the converse is true remains an open problem. Under certain
assumptions on , we show that is non-discrete and
contains rationals (in lowest form) with denominators divisible by arbitrarily
large powers of any prime less than a fixed integer. We explicitly construct
our lattices as fundamental groups of complexes of groups with universal cover
. We conclude with a new proof of an already known analogous result for
regular right-angled buildings
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