4 papers
On the additivity of knot width
Martin Scharlemann, Abigail Thompson
It has been conjectured that the geometric invariant of knots in 3-space called the width is nearly additive. That is, letting w(K) in N denote the width of a knot K in S^3, the co…
Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds
Martin Scharlemann, Abigail Thompson
Understanding non-Haken 3-manifolds is central to many current endeavors in 3-manifold topology. We describe some results for closed orientable surfaces in non-Haken manifolds, and…
Thinning genus two Heegaard spines in the 3-sphere
Martin Scharlemann, Abigail Thompson
We study trivalent graphs in whose closed complement is a genus two handlebody. We show that such a graph, when put in thin position, has a simple (i. e. non-loop) level ed…
Unknotting tunnels and Seifert surfaces
Martin Scharlemann, Abigail Thompson
Let be a knot with an unknotting tunnel and suppose that is not a 2-bridge knot. There is an invariant , odd, defined for the pa…