5 problems

Waldhausen-type conjecture. Every trisection of $S^4$ is isotopic to either the genus $0$ trisection or its stabilization.

Chart simplification conjecture.

Let $(F,\Gamma)$ be a branched covering surface-knot of degree $N$. Let $u_w(F,\Gamma)$ and $u(F,\Gamma)$ denote the weak simplification number and simplification number, respectiv…

Let $(F,\Gamma)$ be a branched covering surface-knot. The quantities $u_w(F,\Gamma)$ and $u(F,\Gamma)$ denote, respectively, the weak simplification number and simplification numbe…

Let $F \subset \mathbf{R}^4$ be an orientable surface knot. Here $w(F)$ denotes the width of $F$, and $\operatorname{Braid}(F)$ denotes its braid index. Width bound conjecture. The…