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Tait's conjectures and odd crossing number amphicheiral knots
Author(s):
A.
Stoimenow
Journal:
Bull. Amer. Math. Soc.
45
(2008),
285-291.
MSC (2000):
Primary 57M25;
Secondary 01A55, 01A60
Posted:
January 22, 2008
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Additional information
Abstract:
We give a brief historical overview of the Tait conjectures, made 120 years ago in the course of his pioneering work in tabulating the simplest knots, and solved a century later using the Jones polynomial. We announce the solution, again based on a substantial study of the Jones polynomial, of one (possibly his last remaining) problem of Tait, with the construction of amphicheiral knots of almost all odd crossing numbers. An application to the non-triviality problem for the Jones polynomial is also outlined.
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Additional Information:
A.
Stoimenow
Affiliation:
Department of Mathematics, Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Email:
stoimeno@kurims.kyoto-u.ac.jp
DOI:
10.1090/S0273-0979-08-01196-8
PII:
S 0273-0979(08)01196-8
Keywords:
Jones polynomial,
amphicheiral knot,
crossing number
Received by editor(s):
May 30, 2007
Posted:
January 22, 2008
Additional Notes:
Financial support by the 21st Century COE Program is acknowledged.
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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