Article
Kyungpook Mathematical Journal 2018; 58(1): 183-202
Published online March 23, 2018
Copyright © Kyungpook Mathematical Journal.
Delta Moves and Arrow Polynomials of Virtual Knots
Myeong–Ju Jeong* and Chan–Young Park
Department of Mathematics, Korea Science Academy 111 Baekyang Gwanmun–Ro, Busanjin–Gu, Busan 614–822, Korea, e-mail : mjjeong@kaist.ac.kr, Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702–701, Korea, e-mail : chnypark@knu.ac.kr
Received: March 16, 2017; Accepted: August 9, 2017
Δ-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 Δ-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 Δ-moves transforming
Keywords: Δ,-move, arrow polynomial, Miyazawa polynomial, virtual knot, Vassiliev invariant