University of Illinois Urbana-Champaign

Finite order automorphisms of Higgs bundles: theory and application

Collier, Brian Patrick

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https://hdl.handle.net/2142/90563

Description

Title
Finite order automorphisms of Higgs bundles: theory and application
Author(s)
Collier, Brian Patrick
Issue Date
2016-04-21
Director of Research (if dissertation) or Advisor (if thesis)
Bradlow, Steve
Doctoral Committee Chair(s)
Nevins, Tom
Committee Member(s)
  • Bergvelt, Maarten
  • Albin, Pierre
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
Graduation Semester
2016-05
Type of Resource
text
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http://hdl.handle.net/2142/90563
Copyright and License Information
Copyright 2016 Brian Collier

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