2 problems

Let $K_1$ and $K_2$ be prime knots in $S^3$, let $t(K)$ denote tunnel number, and let a knot be $\mu$--primitive in the sense used by the source. Prime-knot Morimoto conjecture. ……

Let $L$ be a link with a free decomposing surface $S$, and replace the trivial braids in $N(S)\cap L$ by an arbitrary collection of braids. The resulting link is obtained by braid…