56 citations · 61 across the 7 of their papers we have counts for
4 papers · 1 filter
Thin position in the theory of classical knots
Martin Scharlemann
This is a chapter that is to appear in the "Handbook of Knot Theory", edited by William W. Menasco and Morwen B. Thistlethwaite.
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…
Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting
Martin Scharlemann
An updated proof of a 1933 theorem of Goeritz, exhibiting a finite set of generators for the group of automorphisms of the 3-sphere that preserve a genus two Heegaard splitting. Th…
3-manifolds with planar presentations and the width of satellite knots
Martin Scharlemann, Jennifer Schultens
We consider compact 3-manifolds M having a submersion h to R in which each generic point inverse is a planar surface. The standard height function on a submanifold of the 3-sphere…