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 | References | Similar Articles | Additional Information
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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- [3] K. Murasugi, Jones polynomials of periodic links, Pacific J. Math. 131 (1988), 319-329. MR 922222 (89f:57009)
- [4] P. Traczyk, Periodic knots and the skein polynomial, Invent. Math. 106 (1991), 73-84. MR 1123374 (93e:57014)
- [5] Y. Yokota, The skein polynomial of periodic knots, Math. Ann. 291 (1991), 281-291. MR 1129368 (93c:57010)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1995-1257121-1
Keywords:
Knot,
skein polynomial,
Homfly,
periodic knot,
Jaeger composition product
Article copyright:
© Copyright 1995
American Mathematical Society
