AN ELEMENTARY PROOF OF THE EFFECT OF 3-MOVE ON THE JONES POLYNOMIAL
Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Kim, Soojeong
Cho,,
S.
, &
Kim,,
S.
(2018). AN ELEMENTARY PROOF OF THE EFFECT OF 3-MOVE ON THE JONES POLYNOMIAL. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 25(2), 95-113, https://doi.org/10.7468/jksmeb.2018.25.2.95
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