114 citations · 337 across the 39 of their papers we have counts for
4 papers · 1 filter
Levelling an unknotting tunnel
Hiroshi Goda, Martin Scharlemann, Abigail Thompson
It is a consequence of theorems of Gordon-Reid [Tangle decompositions of tunnel number one knots and links, J. Knot Theory and its Ramifications, 4 (1995) 389-409] and Thompson [Th…
Annuli in generalized Heegaard splittings and degeneration of tunnel number
Martin Scharlemann, Jennifer Schultens
We analyze how a family of essential annuli in a compact 3-manifold will induce, from a strongly irreducible generalized Heegaard splitting of the ambient manifold, generalized Hee…
How a strongly irreducible Heegaard splitting intersects a handlebody
Matt Jones, Martin Scharlemann
It has been shown elsewhere that a strongly irreducible Heegaard splitting surface Q of a compact orientable 3-manifold M can, under reasonable side conditions, intersect a ball or…
The tunnel number of the sum of n knots is at least n
Martin Scharlemann, Jennifer Schultens
We prove that the tunnel number of the sum of n knots is at least n.