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dc.contributor.advisorMargalit, Dan
dc.contributor.authorLanier, Justin Dale
dc.date.accessioned2020-05-20T17:04:43Z
dc.date.available2020-05-20T17:04:43Z
dc.date.created2020-05
dc.date.issued2020-04-27
dc.date.submittedMay 2020
dc.identifier.urihttp://hdl.handle.net/1853/62870
dc.description.abstractA surface of genus g has many symmetries. These form the surface’s mapping class group Mod(S_g), which is finitely generated. The most commonly used generating sets for Mod(S_g) are comprised of infinite order elements called Dehn twists; however, a number of authors have shown that torsion generating sets are also possible. For example, Brendle and Farb showed that Mod(S_g) is generated by six involutions for g ≥ 3. We will discuss our extension of these results to elements of arbitrary order: for k > 5 and g sufficiently large, Mod(S_g) is generated by three elements of order k. Generalizing this idea, in joint work with Margalit we showed that for g ≥ 3 every non-trivial periodic element that is not a hyperelliptic involution normally generates Mod(S_g). This result raises a question: does there exist an N, independent of g, so that if f is a periodic normal generator of Mod(S_g), then Mod(S_g) is generated by N conjugates of f? We show that in general there does not exist such an N, but that there do exist universal bounds when additional conditions are placed on f.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectMapping class groups
dc.subjectGenerating sets
dc.subjectTorsion
dc.titleSmall torsion generating sets for mapping class groups
dc.typeDissertation
dc.description.degreePh.D.
dc.contributor.departmentMathematics
thesis.degree.levelDoctoral
dc.contributor.committeeMemberBelegradek, Igor
dc.contributor.committeeMemberBrendle, Tara E.
dc.contributor.committeeMemberEtnyre, John B.
dc.contributor.committeeMemberHom, Jennifer
dc.date.updated2020-05-20T17:04:43Z


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