4 problems

Juhász–Zemke conjecture. The maps $\widehat{F}_{W,\mathcal{F}}$ coincide with the maps $F_{W,\mathcal{F}}$ defined by Juhász using sutured Floer homology.

Let $L$ be a link and let $L'$ be obtained from $L$ by Conway mutation. Write $\operatorname{\widehat{HFL}}(L)$ and $\operatorname{\widehat{HFL}}(L')$ for their link Floer homologi…

Functoriality conjecture. Link Floer homology is functorial with respect to marked smooth isotopy classes of surfaces embedded in four-space: a marked surface with boundary…

Braid-group action conjecture. The two automorphisms $\rho(\sigma_i)$ and $\operatorname{Id}+\Psi_i\Phi_i$ in $\operatorname{Aut}_{N(K(\mathcal{A}_l))}(\mathit{CFL}(Y,L,p))$ are eq…