Morimoto--Sakuma--Yokota's geometric approach to tunnel number one knots
The author introduces the concept of characteristic knots to \(\theta\)-curves with bridge decompositions. For a given knot \(K\) in \(S^3\), a tunnel is defined as an embedded arc in \(S^3\) with endpoints on \(K\) and interior disjoint from \(K\). A knot with an unknotting tunnel is called a tunnel-1 knot. By means of the refinement of Morimoto-Sakuma-Yokota's method of studying tunnel number one knots, another proof is provided for the tunnel number of the Montesinos knots dealt with by Klimenko-Sakuma.
\({\mathbb Z}_2 \oplus {\mathbb Z}_2\)-branched covering
scientific article; zbMATH DE number 1901912
scientific article