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There are no unexpected tunnel number one knots of genus one |
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| Authors: | Martin Scharlemann |
| Institution: | Department of Mathematics, University of California, Santa Barbara, California 93106 |
| Abstract: | We show that the only knots that are tunnel number one and genus one are those that are already known:  -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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