4 problems

Cancellation conjecture. If knots $J$ and $K\#J$ are doubly slice, then $K$ is doubly slice.

Let $n\ge 3$, and let an even $n$-stranded pretzel knot be a pretzel knot $K=P(a_1,\dots,a_n)$ with even parameters in the sense used for pretzel knots. Write $\gamma_c(K)$ for the…

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…

Annulus-twist invariance conjecture. The 4-ball genera satisfy