## Algebraic & Geometric Topology

### Proof of a stronger version of the AJ Conjecture for torus knots

Anh T Tran

#### Abstract

For a knot $K$ in $S3$, the $sl2$–colored Jones function $JK(n)$ is a sequence of Laurent polynomials in the variable $t$ that is known to satisfy non-trivial linear recurrence relations. The operator corresponding to the minimal linear recurrence relation is called the recurrence polynomial of $K$. The AJ Conjecture (see Garoufalidis [Proceedings of the Casson Fest (2004) 291–309]) states that when reducing $t=−1$, the recurrence polynomial is essentially equal to the $A$–polynomial of $K$. In this paper we consider a stronger version of the AJ Conjecture, proposed by Sikora [arxiv:0807.0943], and confirm it for all torus knots.

#### Article information

Source
Algebr. Geom. Topol., Volume 13, Number 1 (2013), 609-624.

Dates
Accepted: 29 October 2012
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715509

Digital Object Identifier
doi:10.2140/agt.2013.13.609

Mathematical Reviews number (MathSciNet)
MR3116382

Zentralblatt MATH identifier
1270.57051

#### Citation

Tran, Anh T. Proof of a stronger version of the AJ Conjecture for torus knots. Algebr. Geom. Topol. 13 (2013), no. 1, 609--624. doi:10.2140/agt.2013.13.609. https://projecteuclid.org/euclid.agt/1513715509

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