The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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AN ELEMENTARY PROOF OF THE EFFECT OF 3-MOVE ON THE JONES POLYNOMIAL

  • Cho, Seobum (College of Medicine, Yonsei University) ;
  • Kim, Soojeong (University College, Yonsei University International Campus)
  • Received : 2017.04.14
  • Accepted : 2018.03.07
  • Published : 2018.05.31
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Abstract

A mathematical knot is an embedded circle in ${\mathbb{R}}^3$. 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.

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References

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