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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An elementary proof of the Traczyk-Yokota criteria for periodic knots


Author: Józef H. Przytycki
Journal: Proc. Amer. Math. Soc. 123 (1995), 1607-1611
MSC: Primary 57M25
MathSciNet review: 1257121
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Abstract: Traczyk used the first coefficient of the skein (Homfly) polynomial to find powerful criteria for r periodic knots. The criteria were extended by Yokota to $ (r - 1)/2$ first coefficients of the skein polynomial. We give here a short, elementary proof of the Traczyk-Yokota criteria. The main tool is the Jaeger composition product, the same product which is a base for Turaev's Hopf algebra structure of links in a handlebody.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1257121-1
PII: S 0002-9939(1995)1257121-1
Keywords: Knot, skein polynomial, Homfly, periodic knot, Jaeger composition product
Article copyright: © Copyright 1995 American Mathematical Society