Algebraic & Geometric Topology

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

Anh T Tran

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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

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

Received: 22 November 2011
Accepted: 29 October 2012
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

colored Jones polynomial $A$–polynomial AJ Conjecture


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.

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