12 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 $Y$.

Extension conjecture. The intersection form on $\pi_2M$ is extended from the integers.

The $10/8$-conjecture. Then

Let $M$ be the Riemannian $4$-manifold and let the cycles in Theorem 1 be the cycles whose intersection pairing is being estimated. Incompressibility conjecture. The condition that…

Let $(P,\lambda)$ be a hermitian, sesquilinear form on a free $\mathbb{Z}[\mathbb{Z}]$-module of rank $2g$, where $g\in\{1,2\}$. A form is surface hyperbolic if it is isometric to…

Let $p$ be a nonnegative integer and $q$ a natural number. The form … can be realized as the intersection form of a closed smooth spin $4$-manifold. Matsumoto's 11/8-conjecture. Th…

Trisected 11/8-conjecture. One has

Let $P_1^l(n)$ be the set of $l$-tuples of non-negative integers summing to $n$, and let $P(\boldsymbol{\lambda})$ denote the orbit of $\boldsymbol{\lambda}$. For a regular…

Let $X$ be the smooth, closed, oriented $4$-manifold under consideration, with signature $\sigma$ and modified Euler characteristic $\tilde \chi$, and let $\Gamma$ denote its inter…

Let $Y$ be a homology $3$-sphere with $(Y)=0$, and let $\frak{ds}(Y)$ be finite. The bounding genus $|Y|$ is the invariant defined using homologically $1$-connected bounding $4$-ma…

Matsumoto's $11/8$-conjecture. The inequality

Let $X$ be a simply-connected $4$-manifold, and let $B$ be an embedded surface in $X$ of genus $g_B$ with self-intersection … Assume that the class $[B]$ is divisible by $2$. Embed…