JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A Formula for the Colored Jones Polynomial of 2-Bridge Knots
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 48, Issue 2,  2008, pp.255-280
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2008.48.2.255
 Title & Authors
A Formula for the Colored Jones Polynomial of 2-Bridge Knots
Takata, Toshie;
  PDF(new window)
 Abstract
We derive a formula for the colored Jones polynomial of 2-bridge knots. For a twist knot, a more explicit formula is given and it leads to a relation between the degree of the colored Jones polynomial and the crossing number.
 Keywords
Knots;Jones polynomial;
 Language
English
 Cited by
 References
1.
G. Burde and H. Zieschang, Knots, Walter de Gruyter & Co.,Berlin, 1985.

2.
K. Habiro, On the quantum $sl_2$ invariants of knots and integral homology spheres, Geometry and Topology Monographs, 4(5)(2000), 55-68.

3.
V. F. R. Jones, A polynomial invariants for knots via von Neumann algebras, Bull. Amer. Math. Soc., N.S.(1985), 103-111.

4.
A. Kawauchi, A survey of Knot Theory, Birkhauser Verlag, Switzerland, 1996

5.
R. Lawrence and O. Ron, On Habiro's cyclotomic expansions of Ohtsuki invariant, (math.GT/0501549).

6.
T. T. Q. Le, The colored Jones polynomial and A-polynomial of two-bridge knots, (math.GT/0407521).

7.
G. Masbaum, Skein-theoretical derivation of some formulas of Habiro, Algebraic and Geomteric Topology, 3(17)(2003), 537-556. crossref(new window)