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Coxeter Groups and Hyperbolic Manifolds

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JournalMathematischen Annalen
DatePublished - 6 May 2004
Issue number1
Volume330
Number of pages23
Pages (from-to)127-150
Original languageEnglish

Abstract

The theory of Coxeter groups is used to provide an algebraic construction of finite volume hyperbolic 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.

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