7 problems

Let $K_0=k4_3$ be the simplest hyperbolic non-2-bridge knot, and let $J_{K_0}(n)$ denote its colored Jones function. Let $a_j(u,v)\in\mathbb Q(u,v)$ be rational functions with rati…

Relative AJ conjecture. For every $\mathcal O\in\mathcal M(\mathcal T)$,

Let $\widehat{A}$ be the noncommutative $q$-difference operator associated with a knot, and let $A$ be its classical $A$-polynomial. AJ-Conjecture. Specializing $q=1$ in the…

Let $K\subseteq S^3$ be a knot. Let $\hat A_K(t,M,L)$ be the noncommutative quantum A-polynomial obtained from the recursion ideal of the colored Jones polynomial, and let…

Let $K\subseteq M$ be a knot inside a closed, oriented $3$-manifold, with hyperbolic complement. Let $\widehat{A}^{\mathbb{C}}_{K}$ denote the non-commutative polynomial arising fr…

Let $K\subset S^3$ be a knot, let $K_q(S^3\setminus K)$ be its Kauffman bracket skein module, and let $J_n(K;q)$ be the colored Jones polynomials. Strong AJ conjecture. The submodu…

Geometric AJ conjecture. The deformation variety $D_K$ and the characteristic variety $\operatorname{ch}({\mathcal{A}}^K)$ are $M$-essentially equal.