There are no unexpected tunnel number one knots of genus one
- Author(s): Scharlemann, Martin;
- et al.
We show that 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- Muñoz and by Morimoto and Sakuma. This confirms a conjecture first made by Goda and Teragaito.