2026-09-20T16:34:26Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/90563 2023-07-11 col_2142_5131 com_2142_5130

DSpace SAF Submission Ingestion Package generated from Vireo submission #9304 on 2016-07-07 at 13:31:11 Made available in DSpace on 2016-07-07T19:54:09Z (GMT). No. of bitstreams: 3 COLLIER-DISSERTATION-2016.pdf: 943323 bytes, checksum: f7c8542394ec846e354178adc07c5c0a (MD5) LICENSE.txt: 4210 bytes, checksum: 1925f0e6e0a75561683a7797eaf20032 (MD5) PROQUEST_LICENSE.txt: 4556 bytes, checksum: 5da0980478834a3b041214400b8ae7c0 (MD5) Previous issue date: 2016-04-21 application/pdf http://hdl.handle.net/2142/90563 en Copyright 2016 Brian Collier Higgs bundles Character varieties Finite order automorphisms of Higgs bundles: theory and application text text Bradlow, Steve Nevins, Tom Bergvelt, Maarten Albin, Pierre Collier, Brian Patrick 2016-07-07T19:54:09Z 2016-07-07T19:54:09Z 2016-04-21 2016-05 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-07-07 without embargo terms The student, Brian Collier, accepted the attached license on 2016-04-18 at 14:26. The student, Brian Collier, submitted this Dissertation for approval on 2016-04-20 at 11:51. This Dissertation was approved for publication on 2016-04-21 at 08:48. Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.