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dc.contributor.advisorMargalit, Dan
dc.contributor.authorShin, Hyunshik
dc.date.accessioned2014-05-22T15:36:07Z
dc.date.available2014-05-22T15:36:07Z
dc.date.created2014-05
dc.date.issued2014-04-08
dc.date.submittedMay 2014
dc.identifier.urihttp://hdl.handle.net/1853/51910
dc.description.abstractGiven a closed surface Sg of genus g, a mapping class f in \MCG(Sg) is said to be pseudo-Anosov if it preserves a pair of transverse measured foliations such that one is expanding and the other one is contracting by a number \lambda(f). The number \lambda(f) is called a stretch factor (or dilatation) of f. Thurston showed that a stretch factor is an algebraic integer with degree bounded above by 6g-6. However, little is known about which degrees occur. Using train tracks on surfaces, we explicitly construct pseudo-Anosov maps on Sg with orientable foliations whose stretch factor \lambda has algebraic degree 2g. Moreover, the stretch factor \lambda is a special algebraic number, called Salem number. Using this result, we show that there is a pseudo-Anosov map whose stretch factor has algebraic degree d, for each positive even integer d such that d≤g. Our examples also give a new approach to a conjecture of Penner.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectPseudo-Anosov
dc.subjectStretch factor
dc.subjectDilatation
dc.subjectAlgebraic degree
dc.subjectSalem number
dc.subjectTrain track
dc.subject.lcshClass groups (Mathematics)
dc.subject.lcshMappings (Mathematics)
dc.titleAlgebraic degrees of stretch factors in mapping class groups
dc.typeDissertation
dc.description.degreePh.D.
dc.contributor.departmentMathematics
thesis.degree.levelDoctoral
dc.contributor.committeeMemberEtnyre, John
dc.contributor.committeeMemberGaroufalidis, Stavros
dc.contributor.committeeMemberUlmer, Douglas
dc.contributor.committeeMemberWortman, Kevin
dc.date.updated2014-05-22T15:36:07Z


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