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Knots of genus one or on the number of alternating knots of given genus
Author(s):
A.
Stoimenow
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2141-2156.
MSC (2000):
Primary 57M27
Posted:
February 23, 2001
MathSciNet review:
1825928
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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.
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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
DOI:
10.1090/S0002-9939-01-05823-3
PII:
S 0002-9939(01)05823-3
Keywords:
Positive knots,
Seifert surfaces,
Gau\ss{} diagrams,
genus,
unknotting number,
alternating knots,
Vassiliev invariants
Received by editor(s):
February 11, 1999
Received by editor(s) in revised form:
July 23, 1999 and October 20, 1999
Posted:
February 23, 2001
Additional Notes:
The author was supported by a DFG postdoc grant.
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2001,
American Mathematical Society
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