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|dc.description.abstract||Let (W,S) be a Coxeter system with Davis complex Σ. The polyhedral automorphism group G of Σ is a locally compact group under the compact-open topology. If G is a discrete group (as characterised by Haglund-Paulin), then the set Vu(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 Vu(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 Σ. We conclude with a new proof of an already known analogous result for regular right-angled buildings.||en_AU|
|dc.publisher||University of Sydney||en_AU|
|dc.publisher||Faculty of Science||en_AU|
|dc.publisher||School of Mathematics and Statistics||en_AU|
|dc.subject||geometric group theory||en_AU|
|dc.title||A family of uniform lattices acting on a Davis complex with a non-discrete set of covolumes||en_AU|
|dc.type.pubtype||Master of Science M.Sc.||en_AU|
|Appears in Collections:||Sydney Digital Theses (Open Access)|
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