The knot $5_2$ and cyclically presented groups

Goansu Kim; Yangkok Kim; 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. 1998; 35(4): 961-980

Printed December 1, 1998

The knot $5_2$ and cyclically presented groups

Goansu Kim, Yangkok Kim, and Andrei Vesnin

Young Nam University, Dongeui University and Sobolev Institute of Mathematics

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Abstract

The cyclically presented groups which arise as fundamental groups of cyclic branched coverings of the knot $5_2$ are studied. The fundamental polyhedra for these groups are described. Moreover the cyclic covering manifolds are obtained in terms of Dehn surgery and as two-fold branched coverings of the 3-sphere.

Keywords: cyclically presented groups, branched covering, $5_2$ knot

MSC numbers: 57M60