15 citations · 43 across the 11 of their papers we have counts for
4 papers · 2 filters
Surface bundles with genus two Heegaard splittings
Jesse Johnson
It is known that there are surface bundles of arbitrarily high genus which have genus two Heegaard splittings. The simplest examples are Seifert fibered spaces with the sphere as a…
Tunnel number one, genus one fibered knots
Kenneth L. Baker, Jesse E. Johnson, Elizabeth A. Klodginski
We determine the genus one fibered knots in lens spaces that have tunnel number one. We also show that every tunnel number one, once-punctured torus bundle is the result of Dehn fi…
On tunnel number one knots that are not (1,n)
Jesse Johnson, Abigail Thompson
We show that the bridge number of a bridge knot in with respect to an unknotted genus surface is bounded below by a function of the distance of the Heegaard splitting…
Bridge Number and the Curve Complex
Jesse Johnson
We show that there are hyperbolic tunnel-number one knots with arbitrarily high bridge number and that "most" tunnel-number one knots are not one-bridge with respect to an unknotte…