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dc.contributor.advisor Wolf, Michael
dc.creatorLi, Qiongling
dc.date.accessioned 2016-01-25T15:27:41Z
dc.date.available 2016-01-25T15:27:41Z
dc.date.created 2014-12
dc.date.issued 2014-12-04
dc.date.submitted December 2014
dc.identifier.citation Li, Qiongling. "Hitchin Components, Riemannian Metrics and Asymptotics." (2014) Diss., Rice University. https://hdl.handle.net/1911/88090.
dc.identifier.urihttps://hdl.handle.net/1911/88090
dc.description.abstract Higher Teichm\"uller spaces are deformation spaces arising from subsets of the space of representations of a surface group into a general Lie group, e.g., $$PSL(n,\RR)$$, which share some of the properties of classical Teichmueller space. By the non-abelian Hodge theory, such representation spaces correspond to the space of Higgs bundles. We focus on two aspects on the Higher Teichm\"uller space: Riemannian geometry and dynamics. First, we construct a new Riemannian metric on the deformation space for $$PSL(3,\RR)$$, and then prove Teichmueller space endowed with Weil-Petersson metric is totally geodesic in deformation space for $$PSL(3,\RR)$$ with the new metric. Secondly, in a joint work with Brian Collier, we are able to obtain asymptotic behaviors and related properties of representations for certain families of Higgs bundles of rank n.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectHitchin Components
Higgs Bundles
dc.title Hitchin Components, Riemannian Metrics and Asymptotics
dc.type Thesis
dc.contributor.committeeMember Hardt, Robert
dc.contributor.committeeMember Gillman, Adrianna
dc.date.updated 2016-01-25T15:27:41Z
dc.type.material Text
thesis.degree.department Mathematics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy


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