There are no unexpected tunnel number one knots of genus one
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- by Martin Scharlemann PDF
- Trans. Amer. Math. Soc. 356 (2004), 1385-1442 Request permission
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.References
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Additional Information
- Martin Scharlemann
- Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
- MR Author ID: 155620
- Email: mgscharl@math.ucsb.edu
- Received by editor(s): July 24, 2001
- Received by editor(s) in revised form: July 25, 2002
- Published electronically: October 6, 2003
- Additional Notes: This research was supported in part by an NSF grant, the Miller Institute, and RIMS Kyoto
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 356 (2004), 1385-1442
- MSC (2000): Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9947-03-03182-9
- MathSciNet review: 2034312