On the AJ conjecture for cables of twist knots

Anh T. Tran

On the AJ conjecture for cables of twist knots

Geometric Topology 2014-11-19 v3 Quantum Algebra

Authors: Anh T. Tran

Abstract

We study the AJ conjecture that relates the A-polynomial and the colored Jones polynomial of a knot in $S^3$ . We confirm the AJ conjecture for $(r,2)$ -cables of the $m$ -twist knot, for all odd integers $r$ satisfying $\begin{cases} (r+8)(r-8m)>0 &{if~} m> 0, \\ r(r+8m-4)>0 &{if~} m<0.\end{cases}$

Keywords

AJ conjecture A-polynomial colored Jones polynomial twist knots cables $S^3$ knot theory

Cite

@article{arxiv.1409.6071,
  title  = {On the AJ conjecture for cables of twist knots},
  author = {Anh T. Tran},
  journal= {arXiv preprint arXiv:1409.6071},
  year   = {2014}
}

Comments

Results in Section 3 are corrected. arXiv admin note: text overlap with arXiv:1111.5258, arXiv:1405.4055; and with arXiv:math/0407521 by other authors

On the AJ conjecture for cables of twist knots

Abstract

Keywords

Cite

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