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arXiv · 1111.5065

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

Anh T. Tran
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Abstract

For a knot $K$ in $S^3$, the $sl_2$-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.

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Anh T. Tran. 2013-06-16. Proof of a stronger version of the AJ conjecture for torus knots. https://doi.org/10.2140/agt.2013.13.609

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