Cyclic presentations of groups and cyclic branched coverings of (1,1)-knots

Abstract

In this paper we study the connections between cyclic presentations of groups and branched cyclic coverings of (1,1)-knots. In particular, we prove that every n-fold strongly-cyclic branched covering of a (1,1)-knot admits a cyclic presentation for the fundamental group encoded by a Heegaard diagram of genus n.

10 pages, 3 figures. To appear in the Bulletin of the Korean Mathematical Society