The many faces of cyclic branched coverings of 2-bridge knots and links

Details The many faces of cyclic branched coverings of 2-bridge knots and links The many faces of cyclic branched coverings of 2-bridge knots and links

2001-06-19

arxiv.org/abs/math/0106164v1

Mathematics

Geometric Topology

46 pages, 13 figures. To appear in Atti del Seminario Matematico e Fisico dell'Universita' di Modena, special issue dedicated

Scientific paper

We discuss 3-manifolds which are cyclic coverings of the 3-sphere, branched over 2-bridge knots and links. Different descriptions of these manifolds are presented: polyhedral, Heegaard diagram, Dehn surgery and coloured graph constructions. Using these descriptions, we give presentations for their fundamental groups, which are cyclic presentations in the case of 2-bridge knots. The homology groups are given for a wide class of cases. Moreover, we prove that each singly-cyclic branched covering of a 2-bridge link is the composition of a meridian-cyclic branched covering of a determined link and a cyclic branched covering of a trivial knot.

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