English

On the AJ conjecture for cables of the figure eight knot

Geometric Topology 2014-09-03 v4 Quantum Algebra

Abstract

The AJ conjecture relates the A-polynomial and the colored Jones polynomial of a knot in the 3-sphere. It has been verified for some classes of knots, including all torus knots, most double twist knots, (-2,3,6n \pm 1)-pretzel knots, and most cabled knots over torus knots. In this paper we study the AJ conjecture for (r,2)-cables of a knot, where r is an odd integer. In particular, we show that the AJ conjecture holds true for (r,2)-cables of the figure eight knot, where r is an odd integer satisfying |r| \ge 9.

Keywords

Cite

@article{arxiv.1405.4055,
  title  = {On the AJ conjecture for cables of the figure eight knot},
  author = {Anh T. Tran},
  journal= {arXiv preprint arXiv:1405.4055},
  year   = {2014}
}

Comments

New York Journal of Mathematics 20 (2014) 727-741