Manolescu's symplectic link homology conjecture

Let $\kappa$ be a link, let $n>0$, and let ${{\mathscr{H}}_{{(n)} {\scriptscriptstyle{\mathrm{symp}}}}^k}(\kappa)$ denote the link invariant constructed from Lagrangian Floer theory. Let $\mathscr{H}^{i,j}_{(n)}(\kappa^!)$ be the Khovanov–Rozansky homology of the mirror link $\kappa^!$, and let $\mathbb{Q}$ denote the rationals. Manolescu's symplectic link homology conjecture. The invariants are related by

$${{\mathscr{H}}_{{(n)} {\scriptscriptstyle{\mathrm{symp}}}}^k}(\kappa) \otimes \mathbb{Q}=\bigoplus_{i+j=k}\mathscr{H}^{i,j}_{(n)}(\kappa^!).$$

This conjecture proposes that the Floer-theoretic link invariants generalize the construction of Seidel and Smith for $n=2$ and agree, after collapsing the bigrading, with Khovanov–Rozansky homology. Its status is not resolved in the supplied text.