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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An elementary proof of the Traczyk-Yokota criteria for periodic knots
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by Józef H. Przytycki PDF
Proc. Amer. Math. Soc. 123 (1995), 1607-1611 Request permission

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
  • © Copyright 1995 American Mathematical Society
  • 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