Surgery descriptions and volumes of Berge knots I: Large volume Berge knots

Details Surgery descriptions and volumes of Berge knots I: Large volume Berge knots Surgery descriptions and volumes of Berge knots I: Large volume Berge knots

2005-09-02

arxiv.org/abs/math/0509054v1

Mathematics

Geometric Topology

18 pages, 19 figures

Scientific paper

By obtaining surgery descriptions of knots which lie on the genus one fiber
of the trefoil or figure eight knot, we show that these include hyperbolic
knots with arbitrarily large volume. These knots admit lens space surgeries and
form two families of Berge knots. By way of tangle descriptions we also obtain
surgery descriptions for these knots on minimally twisted chain links.

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