Knots of genus one or on the number of alternating knots of given genus
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Abstract:
We prove that any non-hyperbolic genus one knot except the trefoil does not have a minimal canonical Seifert surface and that there are only polynomially many in the crossing number positive knots of given genus or given unknotting number.References
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Additional Information
- A. Stoimenow
- Affiliation: Ludwig-Maximilians University Munich, Mathematics Institute, Theresienstraße 39, 80333 München, Germany
- Address at time of publication: Max Planck Institute of Mathematics, P.O. Box 7280, D-53072 Bonn, Germany
- Email: stoimeno@informatik.hu-berlin.de, alex@mpim-bonn.mpg.de
- Received by editor(s): February 11, 1999
- Received by editor(s) in revised form: July 23, 1999, and October 20, 1999
- Published electronically: February 23, 2001
- Additional Notes: The author was supported by a DFG postdoc grant.
- Communicated by: Ronald A. Fintushel
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2141-2156
- MSC (2000): Primary 57M27
- DOI: https://doi.org/10.1090/S0002-9939-01-05823-3
- MathSciNet review: 1825928