University of Illinois Urbana-Champaign

Gluing constructions for Higgs bundles over a complex connected sum

Kydonakis, Georgios A.

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KYDONAKIS-DISSERTATION-2018.pdf

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

Description

Title
Gluing constructions for Higgs bundles over a complex connected sum
Author(s)
Kydonakis, Georgios A.
Issue Date
2018-04-02
Director of Research (if dissertation) or Advisor (if thesis)
Bradlow, Steven B.
Doctoral Committee Chair(s)
Nevins, Thomas
Committee Member(s)
  • Albin, Pierre
  • Dunfield, Nathan M.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2018-09-04T20:26:48Z
Keyword(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.
Graduation Semester
2018-05
Type of Resource
text
Permalink
http://hdl.handle.net/2142/100920
Copyright and License Information
Copyright 2018 Georgios A. Kydonakis

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