Coxeter Groups and Hyperbolic Manifolds

B. Everitt

doi:10.1007/s00208-004-0543-0

Coxeter Groups and Hyperbolic Manifolds

B. Everitt

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	127-150
Number of pages	23
Journal	Mathematischen Annalen
Volume	330
Issue number	1
DOIs	https://doi.org/10.1007/s00208-004-0543-0
Publication status	Published - 6 May 2004

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10.1007/s00208-004-0543-0

http://dx.doi.org/10.1007/s00208-004-0543-0

Cite this

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title = "Coxeter Groups and Hyperbolic Manifolds",

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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AB - 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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