There are no unexpected tunnel number one knots of genus one

Details There are no unexpected tunnel number one knots of genus one There are no unexpected tunnel number one knots of genus one

2001-06-04

arxiv.org/abs/math/0106017v1

Mathematics

Geometric Topology

73 pp. including 30 figures

Scientific paper

The only knots that are tunnel number one and genus one are those that are
already known: 2-bridge knots obtained by plumbing together two unknotted
annuli and the satellite examples classified by Eudave-Munoz and by
Morimoto-Sakuma. This confirms a conjecture first made by Goda and Teragaito.

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