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Title:Gluing constructions for Higgs bundles over a complex connected sum
Author(s):Kydonakis, Georgios A.
Director of Research:Bradlow, Steven B
Doctoral Committee Chair(s):Nevins, Thomas
Doctoral Committee Member(s):Albin, Pierre; Dunfield, Nathan M
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Higgs bundles, character variety, topological invariants
Abstract: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.
Issue Date:2018-04-02
Type:Thesis
URI:http://hdl.handle.net/2142/100920
Rights Information:Copyright 2018 Georgios A. Kydonakis
Date Available in IDEALS:2018-09-04
Date Deposited:2018-05


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