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Open Access Publications from the University of California

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.

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