56 citations · 61 across the 7 of their papers we have counts for
16 papers
Lecture notes on generalized Heegaard splittings
Toshio Saito, Martin Scharlemann, Jennifer Schultens
These notes grew out of a lecture series given at RIMS in the summer of 2001. The lecture series was aimed at a broad audience that included many graduate students. Its purpose lay…
Proximity in the curve complex: boundary reduction and bicompressible surfaces
Martin Scharlemann
Suppose N is a compressible boundary component of a compact orientable irreducible 3-manifold M and Q is an orientable properly embedded essential surface in M in which each compon…
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…
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…