11 problems

Greene's finiteness conjecture. For every fixed determinant, there exist only finitely many QA links with that determinant.

Let $b$ be an integer, and consider quasi-alternating links whose Jones polynomial has breadth $b$, where the breadth is the difference between the highest and lowest exponents occ…

Qazaqzeh–Chbili–Qublan's conjecture. Every QA Montesinos link satisfies at least one of the following conditions, with strict inequality in the latter two:

No-gap conjecture. If $L$ is a prime quasi-alternating link that is not a $(2,n)$-torus link, then the differential grading of $\mathcal{H}(L)$ has no gap.

Let $L$ be a quasi-alternating link, and let $c(L)$ denote its crossing number and $\det(L)$ its determinant. Qazaqzeh–Qublan–Jaradat conjecture. Every quasi-alternating link $L$ s…

Kanenobu-knot classification conjecture. The only quasi-alternating Kanenobu knots are

Let $L$ be a quasi-alternating link, let $V_L(t)$ denote its Jones polynomial, and let $\operatorname{breadth}(V_L)$ be the difference between the highest and lowest exponents of…

Chbili–Qazaqzeh's conjecture. The coefficients satisfy

Let $L$ be a link whose Jones polynomial is written as … where $m\geq 0$, $a_0\neq 0$, and $a_m\neq 0$. Chbili–Qazaqzeh conjecture. If $L$ is a prime quasi-alternating link, other…

Qazaqzeh–Chbili–Qublan's conjecture. This family is the complete set of quasi-alternating Montesinos links.

Breadth–determinant conjecture. If $L$ is a quasi-alternating link, then