3 problems

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…

Let $K$ be a knot in $S^3$. A concordance is a cobordism of minimal intrinsic complexity, and it has minimal extrinsic complexity when it has no index $2$ Morse critical points. Sl…

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…