David Bachman
Surfaces that become isotopic after Dehn filling.
Втр, 01/26/2010 - 16:01 — SomNambulAuthors: David Bachman, Ryan Derby-Talbot, Eric Sedgwick
Subjects: Geometric Topology
AbstractWe show that after generic filling along a torus boundary component of a
3-manifold, no two closed, 2-sided, essential surfaces become isotopic, and no
closed, 2-sided, essential surface becomes inessential. That is, the set of
essential surfaces (considered up to isotopy) survives unchanged in all
suitably generic Dehn fillings. Furthermore, for all but finitely many
non-generic fillings, we show that two essential surfaces can only become
isotopic in a constrained way.Heegaard structure respects complicated JSJ decompositions.
Пнд, 11/30/2009 - 16:01 — SomNambulAuthors: David Bachman, Ryan Derby-Talbot, Eric Sedgwick
Subjects: Geometric Topology
AbstractLet $M$ be a 3-manifold with torus boundary components $T_1$ and $T_2$. Let
$\phi \colon T_1 \to T_2$ be a homeomorphism, $M_\phi$ the manifold obtained
from $M$ by gluing $T_1$ to $T_2$ via the map $\phi$, and $T$ the image of
$T_1$ in $M_\phi$. We show that if $\phi$ is "sufficiently complicated" then
any incompressible or strongly irreducible surface in $M_\phi$ can be isotoped
to be disjoint from $T$.- Читать далее
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On the existence of high index topologically minimal surfaces.
Ср, 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.
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