3 problems

Reducible-handlebody-link conjecture. Every non-split, reducible handlebody link admits a minimal diagram with $1$-connectivity.

Decomposable-handlebody-link conjecture. Minimal diagrams of a decomposable handlebody link have $2$-connectivity.

A handlebody link $\operatorname{HL}$ is a union of finitely many handlebodies of positive genus embedded in the $3$-sphere $\mathbb S^3$. It is reducible if there is a cutting $2$…