Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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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)
  • Received : 2013.08.20
  • Accepted : 2013.12.31
  • Published : 2014.12.23
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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.

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References

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