{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/57091"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/57091","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"The Enhanced Linking Number and its Applications","abstract":"A \\emph{knot} is the image of an embedding of $S^1$ into $\\R^3$, and a \\emph{link} is the disjoint union of multiple knots. Most of the thesis is spent studying knots and two-component links. Knot theory is concerned with classifying knots and links, and we discuss three notions of equivalence. \\emph{Homotopy} is a weak equivalence that classifies links only up to number of components. \\emph{Link homotopy} is stronger and preserves a notion of inter-component linking. \\emph{Isotopy} is the strongest class of equivalence that preserves all notions of intra-component knotting and inter-component linking.","abstract_html":"A \\emph{knot} is the image of an embedding of <span class=\"etd-inline-math\">S<sup>1</sup></span> into <span class=\"etd-inline-math\">\\R<sup>3</sup></span>, and a \\emph{link} is the disjoint union of multiple knots. Most of the thesis is spent studying knots and two-component links. Knot theory is concerned with classifying knots and links, and we discuss three notions of equivalence. \\emph{Homotopy} is a weak equivalence that classifies links only up to number of components. \\emph{Link homotopy} is stronger and preserves a notion of inter-component linking. \\emph{Isotopy} is the strongest class of equivalence that preserves all notions of intra-component knotting and inter-component linking.","abstract_has_math":true,"creators":["Palesis, Eleni Panayiota"],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-27T22:01:52Z","subjects":["algebra"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/57091","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Palesis, Eleni Panayiota"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-06-23T08:35:31Z"]},{"key":"dc:date.issued","label":"Date","values":["2015"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["algebra"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/57091"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A \\emph{knot} is the image of an embedding of $S^1$ into $\\R^3$, and a \\emph{link} is the disjoint union of multiple knots. Most of the thesis is spent studying knots and two-component links. Knot theory is concerned with classifying knots and links, and we discuss three notions of equivalence. \\emph{Homotopy} is a weak equivalence that classifies links only up to number of components. \\emph{Link homotopy} is stronger and preserves a notion of inter-component linking. \\emph{Isotopy} is the strongest class of equivalence that preserves all notions of intra-component knotting and inter-component linking."]},{"key":"dc:title","label":"Title","values":["The Enhanced Linking Number and its Applications"]}]}],"canonical_facts":{"dc:creator":["Palesis, Eleni Panayiota"],"dc:date.accessioned":["2015-06-23T08:35:31Z"],"dc:date.issued":["2015"],"dc:description.abstract":["A \\emph{knot} is the image of an embedding of $S^1$ into $\\R^3$, and a \\emph{link} is the disjoint union of multiple knots. Most of the thesis is spent studying knots and two-component links. Knot theory is concerned with classifying knots and links, and we discuss three notions of equivalence. \\emph{Homotopy} is a weak equivalence that classifies links only up to number of components. \\emph{Link homotopy} is stronger and preserves a notion of inter-component linking. \\emph{Isotopy} is the strongest class of equivalence that preserves all notions of intra-component knotting and inter-component linking."],"dc:identifier.uri":["http://hdl.handle.net/10339/57091"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["algebra"],"dc:title":["The Enhanced Linking Number and its Applications"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:01:52Z"}