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Delta moves and Kauffman polynomials of virtual knots

Myeong-Ju Jeong

Department of Mathematics, Korea Science Academy of KAIST, Busan, 614-822, Republic of Korea

https://doi.org/10.1142/S0218216514500539Cited by:1 (Source: Crossref)

Abstract

In 1990, 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 Δ-move. We extend the Okada's result for virtual knots by using a Vassiliev invariant v₂ of virtual knots of degree 2 which is induced from the Kauffman polynomial of a virtual knot. We show that v₂(K₁) - v₂(K₂) = ±48, if K₂ is a virtual knot obtained from a virtual knot K₁ by applying a Δ-move. From this we have a lower bound for the number of Δ-moves if two virtual knots K₁ and K₂ are related by a sequence of Δ-moves.

Keywords:

AMSC: 57M25, 57M27

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