Gluing constructions for Higgs bundles over a complex connected sum

For a compact Riemann surface of genus $g\ge 2$, the components of the moduli space of $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-Higgs bundles, or equivalently the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-character variety, are partially labeled by an integer $d$ known as the Toledo invariant. The subspace for which this integer attains a maximum has been shown to have 3\cdot {{2}^2g}+2g-4 many components. A gluing construction between parabolic Higgs bundles over a connected sum of Riemann surfaces provides model Higgs bundles in a subfamily of particular significance. This construction is formulated in terms of solutions to the Hitchin equations, using the linearization of a relevant elliptic operator.

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

2018

Author dc:creator

• Kydonakis, Georgios A.

Contributors dc:contributor

• Bradlow, Steven B.
• Nevins, Thomas
• Albin, Pierre
• Dunfield, Nathan M.

• Higgs bundles, character variety, topological invariants

Statement dc:rights

• Copyright 2018 Georgios A. Kydonakis

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/100920

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/100920