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: | Text |

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 |