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

Abstract

For a knot $K$ in $S^3$, the $s{l}_2$-colored Jones function $J_K(n)$ is a sequence of Laurent polynomials in the variable $t$, which 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 \cite{Ga04} 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 \cite{Si}, and confirm it for all torus knots.

Very minor changes. To appear in Algebraic and Geometric Topology

References in corpus (2)

• The colored Jones function is q-holonomic
• Difference equation of the colored Jones polynomial for torus knot

Cited by in corpus (2)

• The AJ-conjecture and cabled knots over the figure eight knot
• Character varieties, A-polynomials, and the AJ Conjecture