8 problems

For integers $p,q,p',q'$ defining nontrivial torus knots with $g(p,q)=g(p',q')$, let $F(p,q;p',q')$ be the fiber sum along a regular fiber of the rational surfaces $Z(p,q)$ and…

Let $X$ be a simply-connected, almost complex $4$-manifold of Seiberg–Witten simple type, with characteristic numbers $c_1^2$ and $\chi_h$. Fintushel–Stern conjecture. If … then…

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…

Ozbagci–Stipsicz conjecture. For any mapping class in $\Gamma_g^n$, there is an a priori upper bound on the length of any positive factorization of that mapping class.

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…

Symplecticity conjecture. The manifolds $M_{10}$ and $M_{8}$ are symplectic and hence minimal.