4 problems

Finite-index geometric automorphism conjecture. Suppose $M$ has symplectic structures and $A(\Gamma_M)$ is infinite. Then $D(M)$ is of finite index if and only if $M$ is either a K…

Generalised Taubes conjecture. The singular locus $L$ is a meridionally fibered link.

Let $\Xi(3)$ denote the collection of closed $3$--manifolds with positive, cooriented contact structures. Let $\Xi_{\text{\textsf{embed}}}(3)$ consist of those $(M,\xi)\in\Xi(3)$ t…

Let $X$ be a symplectic $4$-manifold with $b^+(X)\geq 2$. The manifold $X$ has Ozsváth–Szabó simple type if every $\operatorname{spin}^c$ structure $\mathfrak{s}$ for which…