Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Delta Moves and Arrow Polynomials of Virtual Knots

  • Jeong, Myeong-Ju (Department of Mathematics, Korea Science Academy) ;
  • Park, Chan-Young (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
  • Received : 2017.03.16
  • Accepted : 2017.08.09
  • Published : 2018.03.23
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Abstract

${\Delta}-moves$ are closely related with a Vassiliev invariant of degree 2. For classical knots, M. Okada showed that the second coefficients of the Conway polynomials of two knots differ by 1 if the two knots are related by a single ${\Delta}-move$. The first author extended the Okada's result for virtual knots by using a Vassiliev invariant of virtual knots of type 2 which is induced from the Kauffman polynomial of a virtual knot. The arrow polynomial is a generalization of the Kauffman polynomial. We will generalize this result by using Vassiliev invariants of type 2 induced from the arrow polynomial of a virtual knot and give a lower bound for the number of ${\Delta}-moves$ transforming $K_1$ to $K_2$ if two virtual knots $K_1$ and $K_2$ are related by a finite sequence of ${\Delta}-moves$.

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References

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