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.References
- François Jaeger, Composition products and models for the homfly polynomial, Enseign. Math. (2) 35 (1989), no. 3-4, 323–361 (English, with French summary). MR 1039950
- V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987), no. 2, 335–388. MR 908150, DOI 10.2307/1971403
- Kunio Murasugi, Jones polynomials of periodic links, Pacific J. Math. 131 (1988), no. 2, 319–329. MR 922222, DOI 10.2140/pjm.1988.131.319
- PawełTraczyk, Periodic knots and the skein polynomial, Invent. Math. 106 (1991), no. 1, 73–84. MR 1123374, DOI 10.1007/BF01243905
- Yoshiyuki Yokota, The skein polynomial of periodic knots, Math. Ann. 291 (1991), no. 2, 281–291. MR 1129368, DOI 10.1007/BF01445208
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