9 problems

Let $(Y,\xi)$ be a contact $3$-manifold, and let $K$ be a null-homologous knot in $(Y,\xi)$. Say that $K$ realizes the three-dimensional Thurston–Bennequin bound when its maximal T…

Sutured ECH–SFH isomorphism conjecture. There is an isomorphism

A sutured manifold $(M,\gamma)$ may be equipped with a contact structure whose boundary contains the relevant gluing data, giving rise to a contact gluing map in sutured Floer homo…

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 $(M,\Gamma,\xi)$ be a sutured contact manifold, and let $\psi(M,\Gamma,\xi)\in\underline{SHM}(-M,-\Gamma)$ and $EH(M,\Gamma,\xi)\in SFH(-M,-\Gamma)$ denote the monopole Floer a…

Sutured ECH–SFH conjecture. There should be an isomorphism

Nonisolating contact invariant conjecture. Over $\mathbb{Z}$-coefficients, the following are equivalent:

Contact invariant slope conjecture. In general,

Let (\Sigma,{\text{\boldmath alpha}},{\text{\boldmath beta}}) be a sutured Heegaard diagram for {\text{\boldmath Sigma}}(D\times I,T). Write $\mathbb{T}_{\alpha}$ and…