There are no unexpected tunnel number one knots of genus one

Author:
Martin Scharlemann

Journal:
Trans. Amer. Math. Soc. **356** (2004), 1385-1442

MSC (2000):
Primary 57M25

Published electronically:
October 6, 2003

MathSciNet review:
2034312

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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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Additional Information

**Martin Scharlemann**

Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106

Email:
mgscharl@math.ucsb.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-03-03182-9

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

Article copyright:
© Copyright 2003
American Mathematical Society