AN ELEMENTARY PROOF OF THE EFFECT OF 3-MOVE ON THE JONES POLYNOMIAL

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2018, v.25 no.2, pp.95-113

https://doi.org/10.7468/jksmeb.2018.25.2.95

Cho, Seobum (College of Medicine, Yonsei University)
Kim, Soojeong (University College, Yonsei University International Campus)

Cho, Seobum, & Kim, Soojeong. (2018). AN ELEMENTARY PROOF OF THE EFFECT OF 3-MOVE ON THE JONES POLYNOMIAL. 한국수학교육학회지시리즈B:순수및응용수학, 25(2), 95-113, https://doi.org/10.7468/jksmeb.2018.25.2.95

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Abstract

A mathematical knot is an embedded circle in <TEX>${\mathbb{R}}^3$</TEX>. A fundamental problem in knot theory is classifying knots up to its numbers of crossing points. Knots are often distinguished by using a knot invariant, a quantity which is the same for equivalent knots. Knot polynomials are one of well known knot invariants. In 2006, J. Przytycki showed the effects of a n - move (a local change in a knot diagram) on several knot polynomials. In this paper, the authors review about knot polynomials, especially Jones polynomial, and give an alternative proof to a part of the Przytychi's result for the case n = 3 on the Jones polynomial.

keywords: knots and links, 2-string tangle, 3-moves, Jones polynomial

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Vol.25 No.2

AN ELEMENTARY PROOF OF THE EFFECT OF 3-MOVE ON THE JONES POLYNOMIAL

AN ELEMENTARY PROOF OF THE EFFECT OF 3-MOVE ON THE JONES POLYNOMIAL

Abstract

한국수학교육학회지시리즈B:순수및응용수학