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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Pezzimenti, Samantha"],"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":2018,"date_issued":"2018-01-01T08:00:00Z","date_published":"2018-01-01T08:00:00Z","updated_at":"2026-07-24T01:23:46Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.brynmawr.edu/dissertations/196","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Pezzimenti, Samantha"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"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":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://repository.brynmawr.edu/dissertations/196"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Immersed Lagrangian Fillings of Legendrian Submanifolds via Generating Families"]}]}],"canonical_facts":{"dc:creator":["Pezzimenti, Samantha"],"dc:description.abstract":["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.
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