Cyclic presentations of groups and cyclic branched coverings of $(1,1)$-knots
Bull. Korean Math. Soc. 2003 Vol. 40, No. 1, 101-108
Published online March 1, 2003
Michele Mulazzani
University of Bologna
Abstract : In this paper we study the connections between cyclic presentations of groups and cyclic branched 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 $n$.
Keywords : $(1,1)$-knots, cyclic branched coverings, cyclically presented groups, Heegaard diagrams, geometric presentations of groups
MSC numbers : Primary 57M12, 57R65; Secondary 20F05, 57M05, 57M25
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