AN ELEMENTARY PROOF OF THE EFFECT OF 3-MOVE ON THE JONES POLYNOMIAL
Authors
Seobum Cho ; Soojeong Kim
Citation
Pure and Applied Mathematics (한국수학교육학회지시리즈B: 순수 및 응용수학), Vol.25(2) : 95-113, 2018
Journal Title
Pure and Applied Mathematics (한국수학교육학회지시리즈B: 순수 및 응용수학)
Issue Date
2018
Keywords
knots and links ; 2-string tangle ; 3-moves ; Jones polynomial
Abstract
A mathematical knot is an embedded circle in R3. 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.