JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Finite Type Invariants and the Kauffman Bracket Polynomials of Virtual Knots
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 54, Issue 4,  2014, pp.639-653
  • 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;
  PDF(new window)
 Abstract
In [9], 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 [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 -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.
 Keywords
virtual knots;graphical finite type invariants;finite type invariants of virtual knots;
 Language
English
 Cited by
1.
On Gauss diagrams of periodic virtual knots, Journal of Knot Theory and Its Ramifications, 2015, 24, 10, 1540008  crossref(new windwow)
 References
1.
D. Bar-Natan, On the Vassiliev knot invariant, Topology, 34 (1995), 423-427. crossref(new window)

2.
J. S. Birman and X.-S. Lin, Knot polynomials and Vassiliev's invariants, Invent. Math., 111(1993), 225-270. crossref(new window)

3.
L. Brand, Differential and Difference equations, John Wiley & Sons, Inc., New York, London, Sydney, 1966.

4.
M. Goussarov, M. Polyak and O. Viro, Finite type invariants of classical and virtual knots, Topology, 39(2000), 1045-1068. crossref(new window)

5.
V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc., 12(1985), 103-112. crossref(new window)

6.
M.-J. Jeong and C.-Y. Park, Vassiliev invariants and double dating tangles, J. of Knot Theory and Its Ramifications, 11(4)(2002), 527-544. crossref(new window)

7.
M.-J. Jeong and C.-Y. Park, Vassiliev invariants and Knot polynomials, Topology and Its Applications, 124(3)(2002), 505-521. crossref(new window)

8.
L. H. Kauffman, State models and the Jones polynomial, Topology, 26(1987), 395-407. crossref(new window)

9.
L. H. Kauffman, Virtual knot theory, Europ. J. Combinatorics, 20(1999), 663-691. crossref(new window)

10.
H. Murakami, On derivatives of the Jones polynomial, Kobe J. Math., 3(1986), 61-64.

11.
K. Murasugi, Knot Theory and Its Applications, Birkhauser, 1996.

12.
R. Trapp, Twist sequences and Vassiliev invariants, J. Knot Theory and Its Ramif., 3(1994), 391-405. crossref(new window)

13.
V. A. Vassiliev, Cohomology of knot spaces, Theory of Singularities and It's Applications, edited by V. I. Arnold, Advances in Soviet Mathematics, Vol. 1, AMS, 1990.

14.
J. Zhu, On Jones knot invariants and Vassiliev invariants, New Zealand J. Math., 27(1998), 294-299.