9 problems

Let $F$ be a smooth $2$-knot, let $n(F)$ denote its odd Khovanov invariant, and let $\Sigma(F)$ denote the branched double-cover associated to $F$. Miller–Wong's conjecture. For ev…

Let $F$ be a smooth $2$-knot, and let $n(F)$ be the integer-valued odd Khovanov invariant associated to a dotted broken surface diagram of $F$. Let $\Sigma(F)$ denote the branched…

Let a dotted $2$-knot be a dotted embedded $2$-sphere in the $4$-sphere, and let its odd Khovanov Jacobsson number be the invariant obtained from the odd Khovanov theory. Let the b…

Slice-depth inequality conjecture. There exist $2$-knots whose slice depth is greater than their unknotting number.

Let the obstruction to smooth equivariant sliceness constructed in this work be restricted to the topological category and to the appropriate class of periodic 2-knots. Obstruction…

Let $K\subset S^4$ be a smooth 2-knot. Removing a small neighborhood of a point of $K$ gives a smooth link cobordism from the empty link to the unknot $U$, and hence a map … For de…

Unknotting conjecture. If a $2$-knot has infinite cyclic knot group, then it is unknotted.

Kirby's unit 2-knot standardness conjecture. Every unit 2-knot $(\mathbb{CP}^2,\mathcal{K})$ is smoothly isotopic to $(\mathbb{CP}^2,\mathbb{CP}^1)$.

Suzuki's unknotting conjecture. Let $G$ be a $2$-knot in $S^4$ with unknotted equator. Then $G$ is smoothly unknotted.