Identifying tunnel number one knots
Identifying tunnel number one knots
Let $K$ be a knot in $S^{3}$ .The tunnel number $t(K)$ of $K$ is the minimal number of mutually disjoint arcs $\{\tau_{i}\}$ "properly embedded" in the pair $(S^{3}, K)$ such that the complement of an open regular neighbourhood of $K\cup(\cup\tau_{\mathfrak{i}})$ is a handlebody.In the above, if the arc system consists …