THE KNOT $5_2$ AND CYCLICALLY PRESENTED GROUPS

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