4 problems

Let $K$ be a knot and $U$ the unknot. Let $\mathcal{S}(K,U)$ be the unique lexicographically ordered finite sequence of triples in $({\mathbb Z}_{\ge 0})^3$ determining the sets…

A slice knot is a knot in the $3$-sphere that bounds a smoothly embedded disk in the $4$-ball, while a ribbon knot admits such a disk on which the radial function of the $4$-ball h…

Slice-ribbon conjecture. Every slice knot has a ribbon concordance to the unknot.

Let $K$ be the rotational virtual knot depicted in Figure. A rotational virtual knot is rotationally slice if it rotationally bounds a virtual surface of genus zero, and its least…