Rocky Mountain Journal of Mathematics

On the HOMFLY polynomial of 4-plat presentations of knots

Bo-hyun Kwon

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In this paper, a method is given for calculating the HOMFLY polynomials of two bridge knots by using a representation of the braid group $\mathbb {B}_4$ into a group of $3\times 3$ matrices. Also, examples will be given of a 2-bridge knot and a 3-bridge knot that have the same Jones polynomial, but different HOMFLY polynomials.

Article information

Rocky Mountain J. Math., Volume 46, Number 1 (2016), 243-260.

First available in Project Euclid: 23 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds

HOMFLY polynomial $2n$-plat presentation HOMFLY bracket polynomial


Kwon, Bo-hyun. On the HOMFLY polynomial of 4-plat presentations of knots. Rocky Mountain J. Math. 46 (2016), no. 1, 243--260. doi:10.1216/RMJ-2016-46-1-243.

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  • C.C. Adams, The knot book, W.H. Freeman and Co., New York, 1994.
  • J. Birman, Braids, links and mapping class groups, Ann. Math. Stud. 82, Princeton University Press, 1974.
  • P. Freyd, D. Yetter, W.B.R. Lickorish, K. Millett and A. Ocneanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. 12 (1985), 239–246.
  • J.R. Goldman and L.H. Kauffman, Rational tangles, Adv. Appl. Math. 18 (1997), 300–332.
  • T. Kanenobu and T. Sumi, Polynomial invariants of $2$-bridge knots through $22$ crossings, Math. Comp. 60 (1993), 771–778, S17–S28.
  • L.H. Kauffman and S. Lambropoulou, On the classification of rational tangles, Adv. Appl. Math. 33 (2004), 199–237.
  • W.B.R. Lickorish and K.C. Millett, A polynomial invariant of oriented links, Topology 26 (1987), 107–141.
  • P. Przytycki and P. Traczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1988), 115–139.