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Nearly Euclidean Thurston Maps and the Halfspace Theorem

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dc.contributor.authorKim, Daniel Minen
dc.contributor.committeechairFloyd, William J.en
dc.contributor.committeememberBrown, Ezra A.en
dc.contributor.committeememberRossi, John F.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2016-11-15T09:00:31Zen
dc.date.available2016-11-15T09:00:31Zen
dc.date.issued2016-11-14en
dc.description.abstractA Thurston map whose postcritical set consists of exactly four points and for which the local degree at each of its critical points is 2 is called textit{nearly Euclidean}. These maps were specified to parse Thurston's combinatorial characterization of rational functions. We determine an extension of the half-space theorem which provides an open hyperbolic half-space such that the negative reciprocal of any fixed slope value is excluded from the boundary of the half-space.en
dc.description.abstractgeneralThurston proved necessary and sufficient conditions under which a certain class of mappings defined topologically are equivalent, in a precise sense which can be considered less strict than topological conjugacy, to a rational map. The conditions presented in the proof of this theorem are not ones for which computational algorithms are easily admitted in all settings. Nearly Euclidean Thurston maps are a sub-class of the maps to which this theorem is applicable and for which an abundance of information is algorithmically attainable. We extend a theorem in this setting. One main example which speaks to the utility of this extension is in determining when certain rational maps arise as matings of polynomials.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:9218en
dc.identifier.urihttp://hdl.handle.net/10919/73446en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectNearly Euclidean Thurston mapsen
dc.subjecthalf-space theoremen
dc.titleNearly Euclidean Thurston Maps and the Halfspace Theoremen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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