A note on the Lickorish-Millett-Turaev formula for the Kauffman polynomial
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- by Józef H. Przytycki PDF
- Proc. Amer. Math. Soc. 121 (1994), 645-647 Request permission
Abstract:
We use the idea of expressing a nonoriented link as a sum of all oriented links corresponding to the link to present a short proof of the Lickorish-Millett-Turaev formula for the Kauffman polynomial at $z = - a - {a^{ - 1}}$. Our approach explains the observation made by Lickorish and Millett that the formula is the generating function for the linking number of a sublink of the given link with its complementary sublink.References
- William M. Goldman, Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math. 85 (1986), no. 2, 263–302. MR 846929, DOI 10.1007/BF01389091
- Jim Hoste and Józef H. Przytycki, Homotopy skein modules of orientable $3$-manifolds, Math. Proc. Cambridge Philos. Soc. 108 (1990), no. 3, 475–488. MR 1068450, DOI 10.1017/S0305004100069371
- Jim Hoste and Józef H. Przytycki, A survey of skein modules of $3$-manifolds, Knots 90 (Osaka, 1990) de Gruyter, Berlin, 1992, pp. 363–379. MR 1177433 L. H. Kauffman, On knots, Ann. of Math. Stud., vol. 115, Princeton Univ. Press, Princeton, NJ, 1987.
- W. B. R. Lickorish and K. C. Millett, An evaluation of the $F$-polynomial of a link, Differential topology (Siegen, 1987) Lecture Notes in Math., vol. 1350, Springer, Berlin, 1988, pp. 104–108. MR 979335, DOI 10.1007/BFb0081470
- Andrew S. Lipson, Some more states models for link invariants, Pacific J. Math. 152 (1992), no. 2, 337–346. MR 1141800
- H. R. Morton, Problems, Braids (Santa Cruz, CA, 1986) Contemp. Math., vol. 78, Amer. Math. Soc., Providence, RI, 1988, pp. 557–574. MR 975094, DOI 10.1090/conm/078/975094
- V. G. Turaev, The Yang-Baxter equation and invariants of links, Invent. Math. 92 (1988), no. 3, 527–553. MR 939474, DOI 10.1007/BF01393746
- Vladimir G. Turaev, Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. (4) 24 (1991), no. 6, 635–704. MR 1142906
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 645-647
- MSC: Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-1994-1213869-5
- MathSciNet review: 1213869