16 problems

Intersection-lattice conjecture. The conclusion of Corollary still holds, under the same assumptions, if $X$ is allowed to range over the set of all symplectic fillings of $Y$.

Let $Y$ be a $3$-manifold and let $\xi$ be a contact structure on $Y$. The torsion of $(Y,\xi)$, denoted by … is the supremum of the integers $n\geq 1$ for which there exists a con…

Nonfillability conjecture. No contact structure defined by Figure and satisfying conditions is fillable.

Let $Y=Y(e_0;r_1,r_2,\ldots,r_n)$ be a Seifert fibered space that is also a rational homology sphere, and let $\xi$ be a contact structure on $Y$. Seifert filling classification co…

Boundary Dehn twist conjecture. The boundary Dehn twist $\tau_M$ has infinite order in the smooth mapping class group

The $\mathcal{QHB}$ conjecture. If $Y$ admits a symplectic rational homology ball filling, then

Let $W_{p,q}(\mathbf{n})$ denote the minimal symplectic filling of $(L(p,q),\xi_{can})$ corresponding to $\mathbf{n}=(n_1,\ldots,n_k)$ in the parameterizing set…

Let $\mathbb{C}^n/G$ be an isolated terminal singularity, and let $(S^{2n-1}/G,\xi_{\rm std})$ be its contact link. Terminal quotient-link orbifold-filling conjecture. Exact orbifo…

Let $\mathbb{C}^n/G$ be an isolated terminal singularity. Its contact link is $(S^{2n-1}/G,\xi_{\rm std})$. Terminal quotient-link conjecture. The contact link…

The standard contact structure on real projective space is denoted by $(\mathbb{R}\mathbb{P}^{2n-1},\xi_{\rm std})$. Eliashberg's conjecture.…

For $n>2$, consider the tight contact structures $\eta^n_{i,j}$ on $-\Sigma(2,3,6n-1)$ with $0\leq i\leq n-2$, $|j|\leq n-i-2$, and $j\equiv n-i\pmod{2}$, and the tight contact str…

Let $D$ be a circular spherical divisor, meaning a topological divisor consisting of a cycle of spheres, and let $b^+(D)$ denote the positive index of its intersection form. The as…

Planar filling finiteness conjecture. Every planar contact $3$-manifold has at most finitely many distinct deformation classes of minimal symplectic fillings.

Wendl's conjecture. The diffeomorphism type of a Stein or exact filling of $(Y,\xi_{std})$ is unique and is given by the disk cotangent bundle for every $g$.

Let $(X,\omega)$ be a closed symplectic $4$-manifold obtained as a symplectic blowup of $\mathbb{CP}^2$ with the standard Kähler form. Let $D=C_1\cup\cdots\cup C_n\subset X$ be a c…

Let $(M,\xi)$ be a closed contact three-manifold supported by a genus one open book $(S_{1,r},\phi)$, where $\phi$ is pseudo-Anosov and the associated foliations have two singulari…