{"id":{"repo_id":"columbia-diss","oai_identifier":"oai:academiccommons.columbia.edu:10.7916/D8T159R9"},"canonical_url":"https://search.dev.ndltd.org/etd/columbia-diss/oai:academiccommons.columbia.edu:10.7916/D8T159R9","repository":{"repo_id":"columbia-diss","name":"Columbia University","base_url":"https://academiccommons.columbia.edu/oai"},"display":{"title":"Bordered Heegaard Floer Homology, Satellites, and Decategorification","abstract":"We use the methods of bordered Floer homology to provide a formula for both τ and HFK of certain satellite knots. In many cases, this formula determines the 4-ball genus of the satellite knot. In parallel, we explore the structural aspects of the bordered theory, developing the notion of an Euler characteristic for the modules associated to a bordered manifold. The Euler characteristic is an invariant of the underlying space, and shares many properties with the analogous invariants for closed 3-manifolds. We study the TQFT properties of this invariant corresponding to gluing, as well as its connections to sutured Floer homology. As one application, we show that the pairing theorem for bordered Floer homology categorifies the classical Alexander polynomial formula for satellites.","abstract_html":"We use the methods of bordered Floer homology to provide a formula for both τ and HFK of certain satellite knots. In many cases, this formula determines the 4-ball genus of the satellite knot. In parallel, we explore the structural aspects of the bordered theory, developing the notion of an Euler characteristic for the modules associated to a bordered manifold. The Euler characteristic is an invariant of the underlying space, and shares many properties with the analogous invariants for closed 3-manifolds. We study the TQFT properties of this invariant corresponding to gluing, as well as its connections to sutured Floer homology. As one application, we show that the pairing theorem for bordered Floer homology categorifies the classical Alexander polynomial formula for satellites.","abstract_has_math":false,"creators":["Petkova, Tsvetelina Vaneva"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-24T01:44:18Z","subjects":["Mathematics","Floer homology","Euler characteristic","Manifolds (Mathematics)"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.7916/D8T159R9","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Petkova, Tsvetelina Vaneva"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012"]},{"key":"dc:type","label":"Dc Type","values":["Theses"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Floer homology","Euler characteristic","Manifolds (Mathematics)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7916/D8T159R9"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We use the methods of bordered Floer homology to provide a formula for both τ and HFK of certain satellite knots. In many cases, this formula determines the 4-ball genus of the satellite knot. In parallel, we explore the structural aspects of the bordered theory, developing the notion of an Euler characteristic for the modules associated to a bordered manifold. The Euler characteristic is an invariant of the underlying space, and shares many properties with the analogous invariants for closed 3-manifolds. We study the TQFT properties of this invariant corresponding to gluing, as well as its connections to sutured Floer homology. As one application, we show that the pairing theorem for bordered Floer homology categorifies the classical Alexander polynomial formula for satellites."]},{"key":"dc:title","label":"Title","values":["Bordered Heegaard Floer Homology, Satellites, and Decategorification"]}]}],"canonical_facts":{"dc:creator":["Petkova, Tsvetelina Vaneva"],"dc:date":["2012"],"dc:description":["We use the methods of bordered Floer homology to provide a formula for both τ and HFK of certain satellite knots. In many cases, this formula determines the 4-ball genus of the satellite knot. In parallel, we explore the structural aspects of the bordered theory, developing the notion of an Euler characteristic for the modules associated to a bordered manifold. The Euler characteristic is an invariant of the underlying space, and shares many properties with the analogous invariants for closed 3-manifolds. We study the TQFT properties of this invariant corresponding to gluing, as well as its connections to sutured Floer homology. As one application, we show that the pairing theorem for bordered Floer homology categorifies the classical Alexander polynomial formula for satellites."],"dc:identifier":["https://doi.org/10.7916/D8T159R9"],"dc:language":["English"],"dc:subject":["Mathematics","Floer homology","Euler characteristic","Manifolds (Mathematics)"],"dc:title":["Bordered Heegaard Floer Homology, Satellites, and Decategorification"],"dc:type":["Theses"]},"updated_at":"2026-07-24T01:44:18Z"}