Heegaard splittings of toroidal 3-manifolds

dc.contributor.advisorGordon, Cameron, 1945-en
dc.creatorDerby-Talbot, Ryanen
dc.date.accessioned2008-08-28T22:53:09Zen
dc.date.available2008-08-28T22:53:09Zen
dc.date.issued2006en
dc.descriptiontexten
dc.description.abstractThis 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.
dc.description.departmentMathematicsen
dc.format.mediumelectronicen
dc.identifierb61295632en
dc.identifier.oclc72712280en
dc.identifier.urihttp://hdl.handle.net/2152/2517en
dc.language.isoengen
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshThree-manifolds (Topology)en
dc.subject.lcshManifolds (Mathematics)en
dc.titleHeegaard splittings of toroidal 3-manifoldsen
dc.type.genreThesisen

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