[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2014.54.4.639

Finite Type Invariants and the Kauffman Bracket Polynomials of Virtual Knots

Jeong, Myeong-Ju (Department of Mathematics and Computer Science, Korea Science Academy of KAIST)
Park, Chan-Young (Department of Mathematics, Kyungpook National University)
Yeo, Soon Tae (Department of Mathematics, Busan National University)

Publication Information

Kyungpook Mathematical Journal / v.54, no.4, 2014 , pp. 639-653 More about this Journal

Abstract

In [9], Kauffman introduced virtual knot theory and generalized many classical knot invariants to virtual ones. For example, he extended the Jones polynomials $V_K(t)$ of classical links to the f-polynomials $f_K(A)$ of virtual links by using bracket polynomials. In [4], 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 $t(a_1,{\cdots},a_m)$ -sequences of virtual knots. Then we show that the higher derivatives $f_K^{(n)}(a)$ of the f-polynomial $f_K(A)$ of a virtual knot K at any point a are not of finite type unless $n{\leq}1$ and a = 1.

Keywords

virtual knots; graphical finite type invariants; finite type invariants of virtual knots;

Citations & Related Records

Reference

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