56 citations · 77 across the 14 of their papers we have counts for
Showing 2001 · math.GTShow all
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math.GT2001
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…
math.GT2001
The Goda-Teragaito conjecture: an overview
Martin Scharlemann
In math.GT/0106017 it was shown that thin position on Heegaard spines can be a useful tool for analyzing the topology of knots in 3-space. The proof there (specifically, of the God…
math.GT2001
There are no unexpected tunnel number one knots of genus one
Martin Scharlemann
The only knots that are tunnel number one and genus one are those that are already known: 2-bridge knots obtained by plumbing together two unknotted annuli and the satellite exampl…