Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2014.54.4.639
Title & Authors
Finite Type Invariants and the Kauffman Bracket Polynomials of Virtual Knots Jeong, Myeong-Ju; Park, Chan-Young; Yeo, Soon Tae;
In , Kauffman introduced virtual knot theory and generalized many classical knot invariants to virtual ones. For example, he extended the Jones polynomials of classical links to the f-polynomials of virtual links by using bracket polynomials. In , M. Goussarov, M. Polyak and O. Viro introduced finite type invariants of virtual knots. In this paper, we give a necessary condition for a virtual knot invariant to be of finite type by using -sequences of virtual knots. Then we show that the higher derivatives of the f-polynomial of a virtual knot K at any point a are not of finite type unless and a = 1.
virtual knots;graphical finite type invariants;finite type invariants of virtual knots;