Doctor of Philosophy (PhD)
When a Legendrian sub manifold admits a generating family (GF), Sabloff and Traynor proved that there is an isomorphism between the GF-cohomology groups of the Legendrian and the cohomology groups of any GF-compatible embedded Lagrangian filling. In this paper, we show that a similar isomorphism exists for immersed GF-compatible Lagrangian fillings; this imposes restrictions on the minimum number and types of double points for any such filling. We also show that from an immersed GF-cobordisms between Legendrian sub manifolds, there exists a long exact sequence relating the GF-cohomology groups of the two Legendrians and cohomology groups associated with the immersed Lagrangian. In addition, we give some constructions of immersed GF-compatible fillings.
Pezzimenti, Samantha. "Immersed Lagrangian Fillings of Legendrian Submanifolds via Generating Families." PhD Diss., Bryn Mawr College, 2018.