Genus one 1-bridge knots and Dunwoody manifolds

Details Genus one 1-bridge knots and Dunwoody manifolds Genus one 1-bridge knots and Dunwoody manifolds

2000-03-07

arxiv.org/abs/math/0003042v1

Mathematics

Geometric Topology

24 pages, 10 figures

Scientific paper

In this paper we show that all 3-manifolds of a family introduced by M. J. Dunwoody are cyclic coverings of lens spaces (eventually $\bf S^3$), branched over genus one 1-bridge knots. As a consequence, we give a positive answer to the Dunwoody conjecture that all the elements of a wide subclass are cyclic coverings of $\bf S^3$ branched over a knot. Moreover, we show that all branched cyclic coverings of a 2-bridge knot belong to this subclass; this implies that the fundamental group of each branched cyclic covering of a 2-bridge knot admits a geometric cyclic presentation.

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