Strongly-cyclic branched coverings of (1, 1)-knots and cyclic presentations of groups
by
Michele Mulazzani
Department of Mathematics - University of Bologna
Coauthors: Alessia Cattabriga (Department of Mathematics - University of Bologna)

The connections among the cyclic branched coverings of (1, 1)-knots, the mapping class group of the twice punctured torus and the cyclic presentations of groups are presented. The necessary and sufficient conditions for the existence and uniqueness of strongly-cyclic branched coverings of (1, 1)-knots are given. It will be proved that every n-fold strongly-cyclic branched covering of a (1, 1)-knot admits a cyclic presentation for the fundamental group, arising from a Heegaard splitting of genus n. Moreover, an algorithm to produce the cyclic presentation will be illustrated.

Date received: June 27, 2001