2 problems

Let $K$ and $K'$ be knots, let $K\#K'$ denote their connected sum, and let $t(K)$ denote the tunnel number. A knot admits a primitive meridian when its exterior has a minimal genus…

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…