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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Tait's conjectures and odd crossing number amphicheiral knots


Author: A. Stoimenow
Journal: Bull. Amer. Math. Soc. 45 (2008), 285-291
MSC (2000): Primary 57M25; Secondary 01A55, 01A60
Published electronically: January 22, 2008
MathSciNet review: 2383306
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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: http://dx.doi.org/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
Published electronically: January 22, 2008
Additional Notes: Financial support by the 21st Century COE Program is acknowledged.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.