Brent Everitt
Published 2002-05-14, updated 2003-06-17Version 2
The rich theory of Coxeter groups is used to provide an algebraic construction of finite volume hyperbolic n-manifolds. Combinatorial properties of finite images of these groups can be used to compute the volumes of the resulting manifolds. Three examples, in 4,5 and 6-dimensions, are given, each of very small volume, and in one case of smallest possible volume.
Comments: No major changes, just some minor improvements and corrections
Journal: Mathematische Annalen 330 (2004) 127-150
L^2-Betti numbers of branched covers of hyperbolic manifolds
The $\ell^2$-homology of even Coxeter groups
Coxeter groups and meridional rank of links
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