Jesse Johnson
An upper bound on common stabilizations of Heegaard splittings.
Wed, 07/13/2011 - 15:01 — SomNambulAuthors: Jesse Johnson
Subjects: Geometric Topology
AbstractWe show that for any two Heegaard splittings of genus $p$ and $q$ for the
same closed 3-manifold, there is a common stabilization of genus at most 3/2 p
+ 2q - 1. One may compare this to recent examples of Heegaard splittings whose
smallest common stabilizations have genus at least $p+q$ or $p + 1/2 q$
depending on the notion of equivalence.Extending pseudo-Anosov maps to compression bodies.
Tue, 11/02/2010 - 16:01 — SomNambulAuthors: Jesse Johnson, Yair Minsky, Ian Biringer
Subjects: Geometric Topology
AbstractWe show that a pseudo-Anosov map on a boundary component of an irreducible
3-manifold has a power that partially extends to the interior if and only if
its (un)stable lamination is a projective limit of meridians. The proof is
through 3-dimensional hyperbolic geometry, and involves an investigation of
algebraic limits of convex cocompact compression bodies.Heegaard splittings with large subsurface distances.
Wed, 02/17/2010 - 16:01 — SomNambulAuthors: Jesse Johnson, Yair Minsky, Yoav Moriah
Subjects: Geometric Topology
AbstractWe show that sub-surfaces of a Heegaard surface for which the relative Hempel
distance of the splitting is sufficiently high have to appear in any Heegaard
surface of genus bounded by half that distance.Mapping class groups of medium distance Heegaard splittings.
Wed, 10/28/2009 - 16:01 — SomNambulAuthors: Jesse Johnson
Subjects: Geometric Topology
AbstractWe 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 class group of the ambient 3-manifold. This implies
that given two handlebody sets in the curve complex for a surface that are
distance at least four apart, the group of automorphisms of the curve complex
that preserve both handlebody sets is finite.On the existence of high index topologically minimal surfaces.
Wed, 09/16/2009 - 13:15 — SomNambulAuthors: Jesse Johnson, David Bachman
Subjects: Geometric Topology
AbstractThe topological index of a surface was previously introduced by the first
author as the topological analogue of the index of an unstable minimal surface.
Here we show that surfaces of arbitrarily high topological index exist.Flipping bridge surfaces.
Thu, 08/27/2009 - 13:23 — SomNambulAuthors: Jesse Johnson, Maggy Tomova
Subjects: Geometric Topology
AbstractWe show that if $K$ is a knot in $S^3$ and $\Sigma$ is a bridge sphere for
$K$ with high distance and $2n$ punctures, the number of perturbations of $K$
required to interchange the two balls bounded by $\Sigma$ via an isotopy is
$n$. This result is also generalized for a knot in any 3-manifold.
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