Heegaard splittings of toroidal 3-manifolds
Abstract
This dissertation is an investigation into the Stabilization Problem for
Heegaard splittings of toroidal 3-manifolds. In several situations we obtain upper
bounds on the number of stabilizations needed for two Heegaard splittings
of a toroidal 3-manifold to become isotopic. Two corollaries of interest are:
(1) Two strongly irreducible Heegaard splittings of sufficiently large genus of
a graph manifold become isotopic after at most one stabilization of the higher
genus splitting, and (2) Two strongly irreducible Heegaard splittings of genus
g which are obtained by Dehn twisting along a canonical torus in the JSJ decomposition
of a 3-manifold become isotopic after at most 4g−4 stabilizations.
Department
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