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    Heegaard splittings of toroidal 3-manifolds

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    derbytalbotr11839.pdf (994.8Kb)
    Date
    2006
    Author
    Derby-Talbot, Ryan
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    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
    Mathematics
    Description
    text
    URI
    http://hdl.handle.net/2152/2517
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