Weyl groups, lattices and geometric manifolds

Brent Everitt; Robert B. Howlett

doi:10.1007/s10711-009-9354-5

Weyl groups, lattices and geometric manifolds

Brent Everitt, Robert B. Howlett

Mathematics

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

Abstract

By studying the action of the Weyl group of a simple Lie algebra on its root lattice, we construct torsion free subgroups of small and explicitly determined index in a large infinite class of Coxeter groups. One spin-off is the construction of hyperbolic manifolds of very small volume in up to 8 dimensions.

Original language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Geometriae Dedicata
Volume	142
Issue number	1
DOIs	https://doi.org/10.1007/s10711-009-9354-5
Publication status	Published - Oct 2009

Keywords

Coxeter groups
Hyperbolic manifolds
COXETER GROUPS
HYPERBOLIC MANIFOLDS
REFLECTION GROUPS
CONJUGACY CLASSES

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10.1007/s10711-009-9354-5

http://arxiv.org/abs/0802.2981

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abstract = "By studying the action of the Weyl group of a simple Lie algebra on its root lattice, we construct torsion free subgroups of small and explicitly determined index in a large infinite class of Coxeter groups. One spin-off is the construction of hyperbolic manifolds of very small volume in up to 8 dimensions.",

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KW - HYPERBOLIC MANIFOLDS

KW - REFLECTION GROUPS

KW - CONJUGACY CLASSES

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Weyl groups, lattices and geometric manifolds

Abstract

Keywords

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