Rocky Mountain Journal of Mathematics

On the HOMFLY polynomial of 4-plat presentations of knots

Bo-hyun Kwon

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Abstract

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

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

Dates
First available in Project Euclid: 23 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1464035861

Digital Object Identifier
doi:10.1216/RMJ-2016-46-1-243

Mathematical Reviews number (MathSciNet)
MR3506087

Zentralblatt MATH identifier
1347.57015

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

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

Citation

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. https://projecteuclid.org/euclid.rmjm/1464035861


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