{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/371527"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/371527","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Floer theory and spectral networks","abstract":"This thesis consists of two papers. In the first paper, we study the relationship between Gaiotto-Moore-Neitzke's non-abelianization map and Floer theory. Given a complete GMN quadratic differential $\\phi$ defined on a closed Riemann surface $C$, let $\\tilde{C}$ be the complement of the poles of $\\phi$. In the case where the spectral curve $\\Sigma_{\\phi}$ is exact with respect to the canonical Liouville form on $T^{\\ast}\\tilde{C}$, we show that an ``almost flat\" $GL(1;\\mathbb{C})$-local system $\\mathcal{L}$ on $\\Sigma_{\\phi}$ defines a Floer cohomology local system $HF_{\\epsilon}(\\Sigma_{\\phi},\\mathcal{L};\\mathbb{C})$ on $\\tilde{C}$ for $0< \\epsilon\\leq 1$. Then we show that for small enough $\\epsilon$, the non-abelianization of $\\mathcal{L}$ is isomorphic to the family Floer cohomology local system $HF_{\\epsilon}(\\Sigma_{\\phi},\\mathcal{L};\\mathbb{C})$. In the second paper, we extend Groman and Solomon's reverse isoperimetric inequality to pseudoholomorphic curves with punctures at the boundary and whose boundary components lie in a collection of Lagrangian submanifolds with intersections locally modelled on $\\RR^n\\cap (\\RR^{k}\\times \\sqrt{-1}\\RR^{n-k})$ inside $\\CC^n$. Our construction closely follows the methods used by Duval and Abouzaid and corrects an error appearing in the latter approach.","abstract_html":"This thesis consists of two papers. In the first paper, we study the relationship between Gaiotto-Moore-Neitzke&#x27;s non-abelianization map and Floer theory. Given a complete GMN quadratic differential $\\phi$ defined on a closed Riemann surface $C$, let $\\tilde{C}$ be the complement of the poles of $\\phi$. In the case where the spectral curve <span class=\"etd-inline-math\">\\Sigma<sub>\\phi</sub></span> is exact with respect to the canonical Liouville form on <span class=\"etd-inline-math\">T<sup>\\ast</sup>\\tilde{C}</span>, we show that an ``almost flat&quot; $GL(1;\\mathbb{C})$-local system $\\mathcal{L}$ on <span class=\"etd-inline-math\">\\Sigma<sub>\\phi</sub></span> defines a Floer cohomology local system <span class=\"etd-inline-math\">HF<sub>&epsilon;</sub>(\\Sigma<sub>\\phi</sub>,\\mathcal{L};\\mathbb{C})</span> on $\\tilde{C}$ for <span class=\"etd-inline-math\">0&lt; &epsilon;\\leq 1</span>. Then we show that for small enough <span class=\"etd-inline-math\">&epsilon;</span>, the non-abelianization of $\\mathcal{L}$ is isomorphic to the family Floer cohomology local system <span class=\"etd-inline-math\">HF<sub>&epsilon;</sub>(\\Sigma<sub>\\phi</sub>,\\mathcal{L};\\mathbb{C})</span>. In the second paper, we extend Groman and Solomon&#x27;s reverse isoperimetric inequality to pseudoholomorphic curves with punctures at the boundary and whose boundary components lie in a collection of Lagrangian submanifolds with intersections locally modelled on <span class=\"etd-inline-math\">\\RR<sup>n</sup>\\cap (\\RR<sup>k</sup>\\times \\sqrt{-1}\\RR<sup>n-k</sup>)</span> inside <span class=\"etd-inline-math\">\\CC<sup>n</sup></span>. Our construction closely follows the methods used by Duval and Abouzaid and corrects an error appearing in the latter approach.","abstract_has_math":true,"creators":["Nho, Yoon Jae"],"institution":"University of Cambridge","degree_name":null,"degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Keating, ailsa"],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-06-30","date_published":"2024-06-30","updated_at":"2026-07-22T22:24:13Z","subjects":["symplectic","spectral curves","quadratic differentials"],"languages":["eng"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/9bd05024-5745-4459-a316-a591acfbd5b1/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.110686","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Keating, ailsa"]},{"key":"dc:creator","label":"Author","values":["Nho, Yoon Jae"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2024-06-30"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/371527"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["symplectic","spectral curves","quadratic differentials"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/9bd05024-5745-4459-a316-a591acfbd5b1/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.17863/CAM.110686"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/8b4a505d-8edf-4d99-87fe-008763ec0186/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis consists of two papers. In the first paper, we study the relationship between Gaiotto-Moore-Neitzke's non-abelianization map and Floer theory. Given a complete GMN quadratic differential $\\phi$ defined on a closed Riemann surface $C$, let $\\tilde{C}$ be the complement of the poles of $\\phi$. In the case where the spectral curve $\\Sigma_{\\phi}$ is exact with respect to the canonical Liouville form on $T^{\\ast}\\tilde{C}$, we show that an ``almost flat\" $GL(1;\\mathbb{C})$-local system $\\mathcal{L}$ on $\\Sigma_{\\phi}$ defines a Floer cohomology local system $HF_{\\epsilon}(\\Sigma_{\\phi},\\mathcal{L};\\mathbb{C})$ on $\\tilde{C}$ for $0< \\epsilon\\leq 1$. Then we show that for small enough $\\epsilon$, the non-abelianization of $\\mathcal{L}$ is isomorphic to the family Floer cohomology local system $HF_{\\epsilon}(\\Sigma_{\\phi},\\mathcal{L};\\mathbb{C})$. In the second paper, we extend Groman and Solomon's reverse isoperimetric inequality to pseudoholomorphic curves with punctures at the boundary and whose boundary components lie in a collection of Lagrangian submanifolds with intersections locally modelled on $\\RR^n\\cap (\\RR^{k}\\times \\sqrt{-1}\\RR^{n-k})$ inside $\\CC^n$. Our construction closely follows the methods used by Duval and Abouzaid and corrects an error appearing in the latter approach."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["a5024db01c87235a8a71fd14d7bdcae8","87eda9de84448d1f82354d60eee3eb5f"]},{"key":"dc:title","label":"Title","values":["Floer theory and spectral networks"]}]}],"canonical_facts":{"dc:contributor.advisor":["Keating, ailsa"],"dc:creator":["Nho, Yoon Jae"],"dc:date.issued":["2024-06-30"],"dc:description.abstract":["This thesis consists of two papers. In the first paper, we study the relationship between Gaiotto-Moore-Neitzke's non-abelianization map and Floer theory. Given a complete GMN quadratic differential $\\phi$ defined on a closed Riemann surface $C$, let $\\tilde{C}$ be the complement of the poles of $\\phi$. In the case where the spectral curve $\\Sigma_{\\phi}$ is exact with respect to the canonical Liouville form on $T^{\\ast}\\tilde{C}$, we show that an ``almost flat\" $GL(1;\\mathbb{C})$-local system $\\mathcal{L}$ on $\\Sigma_{\\phi}$ defines a Floer cohomology local system $HF_{\\epsilon}(\\Sigma_{\\phi},\\mathcal{L};\\mathbb{C})$ on $\\tilde{C}$ for $0< \\epsilon\\leq 1$. Then we show that for small enough $\\epsilon$, the non-abelianization of $\\mathcal{L}$ is isomorphic to the family Floer cohomology local system $HF_{\\epsilon}(\\Sigma_{\\phi},\\mathcal{L};\\mathbb{C})$. In the second paper, we extend Groman and Solomon's reverse isoperimetric inequality to pseudoholomorphic curves with punctures at the boundary and whose boundary components lie in a collection of Lagrangian submanifolds with intersections locally modelled on $\\RR^n\\cap (\\RR^{k}\\times \\sqrt{-1}\\RR^{n-k})$ inside $\\CC^n$. Our construction closely follows the methods used by Duval and Abouzaid and corrects an error appearing in the latter approach."],"dc:format.checksum.md5":["a5024db01c87235a8a71fd14d7bdcae8","87eda9de84448d1f82354d60eee3eb5f"],"dc:identifier.doi":["https://doi.org/10.17863/CAM.110686"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/8b4a505d-8edf-4d99-87fe-008763ec0186/download"],"dc:language":["eng"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/371527"],"dc:rights":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/9bd05024-5745-4459-a316-a591acfbd5b1/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"dc:subject":["symplectic","spectral curves","quadratic differentials"],"dc:title":["Floer theory and spectral networks"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"]},"updated_at":"2026-07-22T22:24:13Z"}