{"id":{"repo_id":"penn","oai_identifier":"oai:repository.upenn.edu:20.500.14332/30297"},"canonical_url":"https://search.dev.ndltd.org/etd/penn/oai:repository.upenn.edu:20.500.14332/30297","repository":{"repo_id":"penn","name":"University of Pennsylvania","base_url":"https://repository.upenn.edu/server/oai/request"},"display":{"title":"Heegaard Floer Invariants and Cabling","abstract":"A natural question in knot theory is to ask how certain properties of a knot behave under satellite operations. We will focus on the satellite operation of cabling, and on Heegaard Floer-theoretic properties. In particular, we will give a formula for the Ozsvath-Szabo concordance invariant tau of iterated cables of a knot K in terms of the cabling parameters, tau(K), and a new concordance invariant, epsilon(K). We show that, in many cases, varepsilon gives better bounds on the 4-ball genus of a knot that tau alone, and discuss further applications of epsilon. We will also completely classify when the iterated cable of a knot admits a positive L-space surgery.","abstract_html":"A natural question in knot theory is to ask how certain properties of a knot behave under satellite operations. We will focus on the satellite operation of cabling, and on Heegaard Floer-theoretic properties. In particular, we will give a formula for the Ozsvath-Szabo concordance invariant tau of iterated cables of a knot K in terms of the cabling parameters, tau(K), and a new concordance invariant, epsilon(K). We show that, in many cases, varepsilon gives better bounds on the 4-ball genus of a knot that tau alone, and discuss further applications of epsilon. We will also completely classify when the iterated cable of a knot admits a positive L-space surgery.","abstract_has_math":false,"creators":["Hom, Jennifer"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Paul Melvin"],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-16","date_published":"2011-05-16","updated_at":"2026-07-24T03:46:55Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.upenn.edu/handle/20.500.14332/30297","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Paul Melvin"]},{"key":"dc:creator","label":"Author","values":["Hom, Jennifer"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-05-17T06:04:13.000"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-05-22T17:37:06Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2011-04-20T00:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2011-05-16"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation/Thesis"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://repository.upenn.edu/handle/20.500.14332/30297"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A natural question in knot theory is to ask how certain properties of a knot behave under satellite operations. We will focus on the satellite operation of cabling, and on Heegaard Floer-theoretic properties. In particular, we will give a formula for the Ozsvath-Szabo concordance invariant tau of iterated cables of a knot K in terms of the cabling parameters, tau(K), and a new concordance invariant, epsilon(K). We show that, in many cases, varepsilon gives better bounds on the 4-ball genus of a knot that tau alone, and discuss further applications of epsilon. We will also completely classify when the iterated cable of a knot admits a positive L-space surgery."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy (PhD)"]},{"key":"dc:title","label":"Title","values":["Heegaard Floer Invariants and Cabling"]}]}],"canonical_facts":{"dc:contributor.advisor":["Paul Melvin"],"dc:creator":["Hom, Jennifer"],"dc:date":["2023-05-17T06:04:13.000"],"dc:date.accessioned":["2023-05-22T17:37:06Z"],"dc:date.available":["2011-04-20T00:00:00Z"],"dc:date.issued":["2011-05-16"],"dc:description.abstract":["A natural question in knot theory is to ask how certain properties of a knot behave under satellite operations. We will focus on the satellite operation of cabling, and on Heegaard Floer-theoretic properties. In particular, we will give a formula for the Ozsvath-Szabo concordance invariant tau of iterated cables of a knot K in terms of the cabling parameters, tau(K), and a new concordance invariant, epsilon(K). We show that, in many cases, varepsilon gives better bounds on the 4-ball genus of a knot that tau alone, and discuss further applications of epsilon. We will also completely classify when the iterated cable of a knot admits a positive L-space surgery."],"dc:description.degree":["Doctor of Philosophy (PhD)"],"dc:identifier.uri":["https://repository.upenn.edu/handle/20.500.14332/30297"],"dc:title":["Heegaard Floer Invariants and Cabling"],"dc:type":["Dissertation/Thesis"]},"updated_at":"2026-07-24T03:46:55Z"}