7 problems

Let $K\subset S^3$ be a knot. It is slice if it bounds a smooth properly embedded disk in the standard $4$-ball $B^4$, and it is ribbon if it bounds a disk that can be isotoped so…

Let $K$ and $J$ be distinct iterated cables of tight fibered knots, and let $p>1$ and $q_1,q_2$ be distinct integers relatively prime to $p$. Define … where $K_{p,q}$ denotes the…

Let $T_{p,q}$ be the $(p,q)$-torus knot in $S^3$, where $p$ and $q$ are positive coprime integers, and let $K$ be a knot concordant to $T_{p,q}$. A ribbon concordance is a concorda…

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…

Let a link in $S^3$ be ribbon when it bounds a ribbon surface and slice when it bounds a slice surface, and let the ribbon and slice genera be the corresponding minimal genera. Gen…

A knot in $S^3$ is ribbon if it bounds a ribbon disk, and slice if it bounds a properly embedded disk in the 4-ball $D^4$. Slice-ribbon conjecture. A knot in $S^3$ is ribbon if and…

Let $K$ be a pretzel knot. A pretzel knot is simple ribbon if a sequence of simple ribbon moves reduces it to a 1-stranded pretzel knot when it is odd, or to a 2-stranded pretzel k…