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Mathematics  2014 

On the Residual Finiteness Growths of Particular Hyperbolic Manifold Groups

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We give a quantification of residual finiteness for compact hyperbolic 3--manifold and 4--manifold groups that virtually embed in specific right-angled Coxeter groups arising as reflection groups for all right polyhedra in ${\bf H}^3$ and ${\bf H}^4$, respectively. We show for this class of groups that their residual finiteness growths are at most linear in terms of geodesic length.


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