Warping geometric structures and abelianizing SL(2,R) local systems

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dc.contributor.advisorNeitzke, Andrew
dc.contributor.committeeMemberBen-Zvi, David
dc.contributor.committeeMemberDistler, Jacques
dc.contributor.committeeMemberFreed, Daniel
dc.contributor.committeeMemberKeel, Sean
dc.creatorFenyes, Aaron Joshua
dc.date.accessioned2016-10-13T15:56:29Z
dc.date.accessioned2018-01-22T22:30:46Z
dc.date.available2016-10-13T15:56:29Z
dc.date.available2018-01-22T22:30:46Z
dc.date.issued2016-05
dc.date.submittedMay 2016
dc.date.updated2016-10-13T15:56:29Z
dc.description.abstractThe abelianization process of Gaiotto, Hollands, Moore, and Neitzke parameterizes SL(K,C) local systems on a punctured surface by turning them into C^\times local systems, which have a much simpler moduli space. When applied to an SL(2,R) local system describing a hyperbolic structure, abelianization produces an R^\times local system whose holonomies encode the shear parameters of the hyperbolic structure. This dissertation extends abelianization to SL(2,R) local systems on a compact surface, using tools from dynamics to overcome the technical challenges that arise in the compact setting. Thurston's shear parameterization of hyperbolic structures, which has its own technical subtleties on a compact surface, once again emerges as a special case.
dc.description.departmentMathematics
dc.format.mimetypeapplication/pdf
dc.identifierdoi:10.15781/T29G5GF9J
dc.identifier.urihttp://hdl.handle.net/2152/41629
dc.language.isoen
dc.subjectGeometric structures
dc.subjectAbelianization
dc.titleWarping geometric structures and abelianizing SL(2,R) local systems
dc.typeThesis
dc.type.materialtext

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