Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 13, Number 1 (2013), 609-624.
Proof of a stronger version of the AJ Conjecture for torus knots
For a knot in , the –colored Jones function is a sequence of Laurent polynomials in the variable 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 . The AJ Conjecture (see Garoufalidis [Proceedings of the Casson Fest (2004) 291–309]) states that when reducing , the recurrence polynomial is essentially equal to the –polynomial of . 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.
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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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