{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/110739"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/110739","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Hamiltonian non-isotopy between the Clifford torus and the Chekanov torus in $\\R^4$","abstract":"The topic of this expository master's thesis concerns proving the Hamiltonian non-isotopy between the monotone Clifford torus and the Chekanov torus in $\\R^4$ by employing three Hamiltonian isotopy invariants: counting of Maslov index 2 pseudo-holomorphic discs with boundaries lying on the torus [EP], the Hamiltonian invariant associated to versal deformations and symplectic capacity [Ch1], and the Hamiltonian invariant defined by Hamiltonian monodromy group of the torus [Yau].","abstract_html":"The topic of this expository master&#x27;s thesis concerns proving the Hamiltonian non-isotopy between the monotone Clifford torus and the Chekanov torus in <span class=\"etd-inline-math\">\\R<sup>4</sup></span> by employing three Hamiltonian isotopy invariants: counting of Maslov index 2 pseudo-holomorphic discs with boundaries lying on the torus [EP], the Hamiltonian invariant associated to versal deformations and symplectic capacity [Ch1], and the Hamiltonian invariant defined by Hamiltonian monodromy group of the torus [Yau].","abstract_has_math":true,"creators":["Si, Aerim"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Kerman, Ely"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-09-17T02:34:47Z","date_published":"2021-09-17T02:34:47Z","updated_at":"2026-07-22T22:24:52Z","subjects":["Hamiltonian isotopy invariant","Clifford torus","Chekanov torus."],"languages":["en"],"rights":["Copyright 2021 Aerim Si"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/110739","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kerman, Ely"]},{"key":"dc:creator","label":"Author","values":["Si, Aerim"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2021-09-17T02:34:47Z","2023-09-17T02:34:57Z","2021-04-29","2021-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Hamiltonian isotopy invariant","Clifford torus","Chekanov torus."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2021 Aerim Si"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/110739"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The topic of this expository master's thesis concerns proving the Hamiltonian non-isotopy between the monotone Clifford torus and the Chekanov torus in $\\R^4$ by employing three Hamiltonian isotopy invariants: counting of Maslov index 2 pseudo-holomorphic discs with boundaries lying on the torus [EP], the Hamiltonian invariant associated to versal deformations and symplectic capacity [Ch1], and the Hamiltonian invariant defined by Hamiltonian monodromy group of the torus [Yau].","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2023-05-01","The student, Aerim Si, accepted the attached license on 2021-04-24 at 02:49.","The student, Aerim Si, submitted this Thesis for approval on 2021-04-24 at 03:06.","This Thesis was approved for publication on 2021-04-29 at 16:09.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16542 on 2021-09-16 at 17:05:11","Made available in DSpace on 2021-09-17T02:34:47Z (GMT). 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