Legendrian intersections in twisted 1-jet bundles

<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>J¹M</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>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Open Access

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2026

Author dc:creator

• Vargas Jr., Alfredo

Repository record dc:identifier

https://repository.brynmawr.edu/dissertations/270

OAI identifier oai:identifier

oai:repository.brynmawr.edu:dissertations-1282