Finite order automorphisms of Higgs bundles: theory and application

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2016

Author dc:creator

• Collier, Brian Patrick

Contributors dc:contributor

• Bradlow, Steve
• Nevins, Tom
• Bergvelt, Maarten
• Albin, Pierre

• Higgs bundles
• Character varieties

Statement dc:rights

• Copyright 2016 Brian Collier

Language dc:language

en

Handle dc:identifier

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

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F90563