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There are no unexpected tunnel number one knots of genus one
Abstract
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.
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