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Title:Finite order automorphisms of Higgs bundles: theory and application
Author(s):Collier, Brian Patrick
Director of Research:Bradlow, Steve
Doctoral Committee Chair(s):Nevins, Tom
Doctoral Committee Member(s):Bergvelt, Maarten; Albin, Pierre
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Higgs bundles
Character varieties
Abstract:We study G-Higgs bundles over a Riemann surface which are fixed points of a roots of unity action. When G is complex we classify such fixed points and study certain lifting properties of the corresponding harmonic metric. This remainder of the thesis is devoted to applications. In particular, parameterize the space of maximal SO(2,3) surface group representations as fiber bundles over Teichmuller space. We also show that there are many new connected components of the SO(n,n+1) character variety.
Issue Date:2016-04-21
Type:Thesis
URI:http://hdl.handle.net/2142/90563
Rights Information:Copyright 2016 Brian Collier
Date Available in IDEALS:2016-07-07
Date Deposited:2016-05


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