ar X iv : m at h / 99 07 13 9 v 1 [ m at h . G T ] 2 2 Ju l 1 99 9 CONSTRUCTING HYPERBOLIC MANIFOLDS
نویسندگان
چکیده
The Coxeter simplex with symbol is a compact hyperbolic 4-simplex and the related Coxeter group Γ is a discrete subgroup of Isom(H 4). The Coxeter simplex with symbol is a spherical 3-simplex, and the related Coxeter group G is the group of symmetries of the regular 120-cell. Using the geometry of the regular 120-cell, Davis [3] constructed an epimorphism Γ → G whose kernel K was torsion-free, thus obtaining a small volume compact hyperbolic 4-manifold H 4 /K. In this paper we show how to obtain representations Γ → G of Coxeter groups Γ acting on H n to certain classical groups G. We determine when the kernel K of such a homomorphism is torsion-free and thus H n /K is a hyperbolic n-manifold. As an example, this is applied to the two groups described above, with G suitably interpreted as a classical group. Using this, further information on the quotient manifold is obtained.
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