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

Tran, Anh T¹

¹Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus OH 43210, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 1, pp. 609-624

Résumé

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.

Détail

DOI : 10.2140/agt.2013.13.609

Classification : 57N10, 57M25
Keywords: colored Jones polynomial, $A$–polynomial, AJ Conjecture

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