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Bradlow, Steven B. Nevins, Thomas Albin, Pierre Dunfield, Nathan M. Kydonakis, Georgios A. 2018-09-04T20:26:48Z 2018-09-04T20:26:48Z 2018-04-02 2018-05 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-08-31 without embargo terms The student, Georgios Kydonakis, accepted the attached license on 2018-03-31 at 09:22. The student, Georgios Kydonakis, submitted this Dissertation for approval on 2018-03-31 at 09:33. This Dissertation was approved for publication on 2018-04-02 at 11:58. DSpace SAF Submission Ingestion Package generated from Vireo submission #12105 on 2018-08-31 at 17:10:26 Made available in DSpace on 2018-09-04T20:26:48Z (GMT). No. of bitstreams: 3 KYDONAKIS-DISSERTATION-2018.pdf: 1114856 bytes, checksum: 8b2ee8f481d728c6357b1ddfc904a4b0 (MD5) LICENSE.txt: 4215 bytes, checksum: 657631987c143a1797de5e8afcfbb49b (MD5) PROQUEST_LICENSE.txt: 4561 bytes, checksum: f225b7acf388c71665e53d19fec16ef3 (MD5) Previous issue date: 2018-04-02 application/pdf http://hdl.handle.net/2142/100920 en Copyright 2018 Georgios A. Kydonakis Higgs bundles, character variety, topological invariants Gluing constructions for Higgs bundles over a complex connected sum text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.