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

Przytycki, Józef H.

doi:10.1090/S0002-9939-1995-1257121-1

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
DOI: https://doi.org/10.1090/S0002-9939-1995-1257121-1
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 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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