9 problems

Width additivity conjecture. It was conjectured that

Height variation conjecture. There is a knot $K$ such that

Let $B_i$ be the braids occurring in the paper's construction, and let $K_{2,1,3,7}$ and $K_{4,1,3,3}$ denote the corresponding knots. A thin position is an embedding realizing min…

Let $K$ and $K'$ be knots, with embeddings $k$ and $k'$, respectively. An embedding is width-minimizing when it realizes the knot's minimum width; similarly, trunk-minimizing and b…

Let $K$ be a knot in $S^3$, and let an embedding of $K$ have width and trunk measured by $w$ and $tr$, respectively. An embedding is width-minimizing when its width equals $w(K)$,…

Trunk additivity conjecture. It holds that

Height additivity conjecture. It holds that

Let $K$ be a satellite knot with pattern $\hat{K}$ and companion $J$, where $n$ is the winding number of $\hat{K}$. Width bound conjecture. The width satisfies … This is the width…

Scharlemann–Thompson's conjecture. There exist knots $K$ and $2$--bridge knots $K'$ such that