SCHARLEMANN–THOMPSON INVARIANT FOR KNOTS WITH UNKNOTTING TUNNELS AND THE DISTANCE OF (1,1)-SPLITTINGS

Scharlemann and Thompson introduced an invariant ρ(K, γ) ∈ Q/2Z for the pair of a knot K in the 3-sphere and an unknotting tunnel γ for K. The paper studies the relationship between the invariant ρ(K, γ) of a (1, 1)-knot and the distance of its (1, 1)-splitting introduced by the author.