There are no unexpected tunnel number one knots of genus one
Geometric Topology
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0106017,
title = {There are no unexpected tunnel number one knots of genus one},
author = {Martin Scharlemann},
journal= {arXiv preprint arXiv:math/0106017},
year = {2007}
}
Comments
73 pp. including 30 figures