Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

A Formula for the Colored Jones Polynomial of 2-Bridge Knots

  • Takata, Toshie (Department of Mathematics, Faculty of Science, Niigata University)
  • Received : 2006.06.29
  • Published : 2008.06.30
Download PDF
⟨ Previous Next ⟩

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

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. https://doi.org/10.2140/agt.2003.3.537

Cited by

  1. The 𝔰𝔩3 colored Jones polynomials for 2-bridge links vol.26, pp.07, 2017, https://doi.org/10.1142/S0218216517500389