Greene's finiteness conjecture for quasi-alternating links

A quasi-alternating link is a link in the class referred to as quasi-alternating in the source, and $\det(L)$ denotes its determinant. Greene's conjecture. There exist only finitely many quasi-alternating links with a given determinant.

The conjecture is presented as a strengthening of the question of whether there are infinitely many quasi-alternating knots with a given knot Floer homology type. Greene proved the cases in which $\det(L)=1$, $2$, or $3$, while the general statement remains open.