Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A family of uniform lattices acting on a Davis complex with a
  non-discrete set of covolumes   Let $(W,S)$ be a Coxeter system with Davis complex $\Sigma$. The polyhedral
automorphism group $G$ of $\Sigma$ is a locally compact group under the
compact-open topology. If $G$ is a discrete group (as characterised by
Haglund--Paulin), then the set $\mathcal V_u(G)$ of uniform lattices in $G$ is
discrete. Whether the converse is true remains an open problem. Under certain
assumptions on $(W,S)$, we show that $\mathcal V_u(G)$ 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
$\Sigma$. We conclude with a new proof of an already known analogous result for
regular right-angled buildings.

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph