Finite order automorphisms of Higgs bundles: theory and application

Higgs bundles;Character varieties

Collier, Brian Patrick

关键词: Higgs bundles;    Character varieties;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/90563/COLLIER-DISSERTATION-2016.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.