{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/100920"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/100920","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Gluing constructions for Higgs bundles over a complex connected sum","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.","abstract_html":"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 <span class=\"etd-inline-math\">3\\cdot {{2}<sup>2g</sup>}+2g-4</span> 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.","abstract_has_math":true,"creators":["Kydonakis, Georgios A."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Bradlow, Steven B.","Nevins, Thomas","Albin, Pierre","Dunfield, Nathan M."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-04T20:26:48Z","date_published":"2018-09-04T20:26:48Z","updated_at":"2026-07-22T22:24:38Z","subjects":["Higgs bundles, character variety, topological invariants"],"languages":["en"],"rights":["Copyright 2018 Georgios A. Kydonakis"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/100920","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bradlow, Steven B.","Nevins, Thomas","Albin, Pierre","Dunfield, Nathan M."]},{"key":"dc:creator","label":"Author","values":["Kydonakis, Georgios A."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-04T20:26:48Z","2018-04-02","2018-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Higgs bundles, character variety, topological invariants"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Georgios A. Kydonakis"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/100920"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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). 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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). 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