Coxeter groups and branched coverings of lens spaces

Alexander Mednykh; Andrei Vesnin

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2001; 38(6): 1167-1177

Printed November 1, 2001

Coxeter groups and branched coverings of lens spaces

Alexander Mednykh and Andrei Vesnin

Sobolev Institute of Mathematics and

Abstract

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Abstract

The groups generated by reflections in faces of Coxeter polyhedra in three-dimensional Thurston's spaces are considered. We develop a method for finding of finite index subgroups of Coxeter groups which uniformize three-dimensional manifolds obtained as two-fold branched coverings of manifolds of Heegaard genus one, that are lens spaces $L(p, q)$ and the space $S^2\times S^1$.

Keywords: Coxeter group, link, lens space, 3-orbifold, branched covering, geometric structure