The Arnold conjecture for Lagrangian intersections in the setting of cotangent bundles with their standard symplectic structure has long been settled, as has its contact analog for Legendrian intersections in the setting of 1-jet bundles with their standard contact structure. This latter result was due originally to Chekanov, and was later refined by Bhupal. More recently, Chantraine and Murphy proved an analog of the Arnold conjecture for Lagrangian intersections in cotangent bundles with respect to their standard LCS (locally conformally symplectic) structures. This dissertation establishes a refinement of Chantraine and Murphy’s theorem analogous to Bhupal’s refinement of Chekanov’s theorem, where instead of the standard contact structure on J1M we work with respect to the “twisted” contact structure lifting a given standard LCS structure on the underlying cotangent bundle. The proof involves defining an extension of the classical action functional in order to establish a variational principle for contact isotopies in the twisted sense, then carefully leveraging this to obtain special finite dimensional generating families, with explicitly calculable Morse index, for the associated Legendrians.
","abstract_html":"<p>The Arnold conjecture for Lagrangian intersections in the setting of cotangent bundles with their standard symplectic structure has long been settled, as has its contact analog for Legendrian intersections in the setting of 1-jet bundles with their standard contact structure. This latter result was due originally to Chekanov, and was later refined by Bhupal. More recently, Chantraine and Murphy proved an analog of the Arnold conjecture for Lagrangian intersections in cotangent bundles with respect to their standard <em>LCS</em> (<em>locally conformally symplectic</em>) structures. This dissertation establishes a refinement of Chantraine and Murphy’s theorem analogous to Bhupal’s refinement of Chekanov’s theorem, where instead of the standard contact structure on <em>J<sup>1</sup>M</em> we work with respect to the “twisted” contact structure lifting a given standard LCS structure on the underlying cotangent bundle. The proof involves defining an extension of the classical action functional in order to establish a variational principle for contact isotopies in the twisted sense, then carefully leveraging this to obtain special finite dimensional generating families, with explicitly calculable Morse index, for the associated Legendrians.</p>","abstract_has_math":false,"creators":["Vargas Jr., Alfredo"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Open Access","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026-01-01T08:00:00Z","date_published":"2026-01-01T08:00:00Z","updated_at":"2026-07-24T01:23:53Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.brynmawr.edu/dissertations/270","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Vargas Jr., Alfredo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2028-05-07T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://repository.brynmawr.edu/dissertations/270"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Arnold conjecture for Lagrangian intersections in the setting of cotangent bundles with their standard symplectic structure has long been settled, as has its contact analog for Legendrian intersections in the setting of 1-jet bundles with their standard contact structure. This latter result was due originally to Chekanov, and was later refined by Bhupal. More recently, Chantraine and Murphy proved an analog of the Arnold conjecture for Lagrangian intersections in cotangent bundles with respect to their standard LCS (locally conformally symplectic) structures. This dissertation establishes a refinement of Chantraine and Murphy’s theorem analogous to Bhupal’s refinement of Chekanov’s theorem, where instead of the standard contact structure on J1M we work with respect to the “twisted” contact structure lifting a given standard LCS structure on the underlying cotangent bundle. The proof involves defining an extension of the classical action functional in order to establish a variational principle for contact isotopies in the twisted sense, then carefully leveraging this to obtain special finite dimensional generating families, with explicitly calculable Morse index, for the associated Legendrians.
"]},{"key":"dc:title","label":"Title","values":["Legendrian intersections in twisted 1-jet bundles"]}]}],"canonical_facts":{"dc:creator":["Vargas Jr., Alfredo"],"dc:date.available":["2028-05-07T07:00:00Z"],"dc:description.abstract":["The Arnold conjecture for Lagrangian intersections in the setting of cotangent bundles with their standard symplectic structure has long been settled, as has its contact analog for Legendrian intersections in the setting of 1-jet bundles with their standard contact structure. This latter result was due originally to Chekanov, and was later refined by Bhupal. More recently, Chantraine and Murphy proved an analog of the Arnold conjecture for Lagrangian intersections in cotangent bundles with respect to their standard LCS (locally conformally symplectic) structures. This dissertation establishes a refinement of Chantraine and Murphy’s theorem analogous to Bhupal’s refinement of Chekanov’s theorem, where instead of the standard contact structure on J1M we work with respect to the “twisted” contact structure lifting a given standard LCS structure on the underlying cotangent bundle. The proof involves defining an extension of the classical action functional in order to establish a variational principle for contact isotopies in the twisted sense, then carefully leveraging this to obtain special finite dimensional generating families, with explicitly calculable Morse index, for the associated Legendrians.
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