9 problems

Let $L$ be a smooth link. Call $L$ orientably exact Lagrangian fillable if it has a Legendrian representative in the standard contact $\mathbb{R}^3$ admitting an orientable exact L…

Strong quasipositivity conjecture. A link $L$ is strongly quasipositive if and only if it is Bennequin-sharp.

Boileau–Boyer–Gordon conjecture. Every fibred strongly quasipositive link whose cyclic branched cover is an L-space is simply laced arborescent; examples include the two-strand tor…

Quasipositivity under braid connected sum. $X$ is quasipositive if and only if $X_1$ and $X_2$ are quasipositive.

Defect-zero characterization conjecture.

The branched-cover L-space conjecture. If some $\Sigma_n(L)$ is an L-space, then $L$ is simply laced arborescent. If $L=K$ is a knot, then $K$ is a $(2,k)$, $(3,4)$, or $(3,5)$ tor…

Let $(Y,\xi)$ be a contact $3$-manifold and let a transverse link in $(Y,\xi)$ be given. A Seifert surface for the link has a Morse-Smale characteristic foliation with positive sin…

A transverse $\mathbb{C}$-link in $S^3$ is a link arising as the transverse intersection of a smooth complex curve with the unit sphere in $\mathbb{C}^2$. Rudolph's conjecture. Eve…

Let $L$ be a non-splittable unoriented link in $S^3$. An orientation of $L$ is strongly quasipositive if the oriented link bounds a strongly quasipositive surface. Two-orientation…