14 citations · 20 across the 5 of their papers we have counts for
6 papers · 1 filter
Mapping class groups of medium distance Heegaard splittings
Jesse Johnson
We show that if the Hempel distance of a Heegaard splitting is larger than three then the mapping class group of the Heegaard splitting is isomorphic to a subgroup of the mapping c…
Flipping and stabilizing Heegaard splittings
Jesse Johnson
We show that the number of stabilizations needed to interchange the handlebodies of a Heegaard splitting of a closed 3-manifold by an isotopy is bounded below by the smaller of twi…
Horizontal Heegaard splittings of Seifert fibered spaces
Jesse Johnson
We show that if an orientable Seifert fibered space with an orientable genus base space admits a strongly irreducible horizontal Heegaard splitting then there is a one-to-o…
Automorphisms of the three-torus preserving a genus three Heegaard splitting
Jesse Johnson
The mapping class group of a Heegaard splitting is the group of connected components in the set of automorphisms of the ambient manifold that map the Heegaard surface onto itself.…
Generalized handlebody sets and non-Haken 3-manifolds
Jesse Johnson, Terk Patel
In the curve complex for a surface, a handlebody set is the set of loops that bound properly embedded disks in a given handlebody bounded by the surface. A boundary set is the set…
Stable functions and common stabilizations of Heegaard splittings
Jesse Johnson
We present a new proof of Reidemeister and Singer's Theorem that any two Heegaard splittings of the same 3-manifold have a common stabilization. The proof leads to an upper bound o…