Unknotting tunnels and Seifert surfaces

Martin Scharlemann, Abigail Thompson

Let $K$ be a knot with an unknotting tunnel $\gamma$ and suppose that $K$ is not a 2-bridge knot. There is an invariant $\rho =p/q\in \mathbb{Q}/2\mathbb{Z}$, $p$ odd, defined for the pa…