{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/78347"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/78347","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Symplectic circle actions with isolated fixed points","abstract":"Consider a symplectic circle action on a closed symplectic manifold $M$ with non-empty isolated fixed points. Associated to each fixed point, there are well-defined non-zero integers, called \\emph{weights}. We prove that the action is Hamiltonian if the sum of an odd number of weights is never equal to the sum of an even number of weights (the weights may be taken at different fixed points). Moreover, we show that if $\\dim M=6$, or if $\\dim M=2n \\leq 10$ and each fixed point has weights $\\{\\pm a_1, \\cdots, \\pm a_n\\}$ for some positive integers $a_i$, the action is Hamiltonian if the sum of three weights is never equal to zero. As applications, we recover the results for semi-free actions, and for certain circle actions on six-dimensional manifolds. Finally, we prove that if there are exactly three fixed points, $M$ is equivariantly symplectomorphic to $\\mathbb{CP}^{2}$.","abstract_html":"Consider a symplectic circle action on a closed symplectic manifold $M$ with non-empty isolated fixed points. Associated to each fixed point, there are well-defined non-zero integers, called \\emph{weights}. We prove that the action is Hamiltonian if the sum of an odd number of weights is never equal to the sum of an even number of weights (the weights may be taken at different fixed points). Moreover, we show that if $\\dim M=6$, or if $\\dim M=2n \\leq 10$ and each fixed point has weights <span class=\"etd-inline-math\">\\{\\pm a<sub>1</sub>, \\cdots, \\pm a<sub>n</sub>\\}</span> for some positive integers <span class=\"etd-inline-math\">a<sub>i</sub></span>, the action is Hamiltonian if the sum of three weights is never equal to zero. As applications, we recover the results for semi-free actions, and for certain circle actions on six-dimensional manifolds. Finally, we prove that if there are exactly three fixed points, $M$ is equivariantly symplectomorphic to <span class=\"etd-inline-math\">\\mathbb{CP}<sup>2</sup></span>.","abstract_has_math":true,"creators":["Jang, Donghoon"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Tolman, Susan","Lerman, Eugene","Kerman, Ely","Leininger, Christopher J."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-07-22T22:16:27Z","date_published":"2015-07-22T22:16:27Z","updated_at":"2026-07-22T22:26:11Z","subjects":["symplectic circle action","fixed points","Hamiltonian circle action","weights"],"languages":["en"],"rights":["Copyright 2015 Donghoon Jang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/78347","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Tolman, Susan","Lerman, Eugene","Kerman, Ely","Leininger, Christopher J."]},{"key":"dc:creator","label":"Author","values":["Jang, Donghoon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-07-22T22:16:27Z","2015-05","2015-04-07","2015-5"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"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":["symplectic circle action","fixed points","Hamiltonian circle action","weights"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 Donghoon Jang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/78347"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Consider a symplectic circle action on a closed symplectic manifold $M$ with non-empty isolated fixed points. Associated to each fixed point, there are well-defined non-zero integers, called \\emph{weights}. We prove that the action is Hamiltonian if the sum of an odd number of weights is never equal to the sum of an even number of weights (the weights may be taken at different fixed points). Moreover, we show that if $\\dim M=6$, or if $\\dim M=2n \\leq 10$ and each fixed point has weights $\\{\\pm a_1, \\cdots, \\pm a_n\\}$ for some positive integers $a_i$, the action is Hamiltonian if the sum of three weights is never equal to zero. As applications, we recover the results for semi-free actions, and for certain circle actions on six-dimensional manifolds. Finally, we prove that if there are exactly three fixed points, $M$ is equivariantly symplectomorphic to $\\mathbb{CP}^{2}$.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-07-22 without embargo terms","The student, Donghoon Jang, accepted the attached license on 2015-04-02 at 18:05.","The student, Donghoon Jang, submitted this Dissertation for approval on 2015-04-02 at 18:09.","This Dissertation was approved for publication on 2015-04-07 at 14:20.","DSpace SAF Submission Ingestion Package generated from Vireo submission #7785 on 2015-07-22 at 10:31:25","Made available in DSpace on 2015-07-22T22:16:27Z (GMT). No. of bitstreams: 2 JANG-DISSERTATION-2015.pdf: 496326 bytes, checksum: b3cf126c5fe63cba160877ca04608b19 (MD5) LICENSE.txt: 4210 bytes, checksum: 70bf9842746d3996058376223117fdcf (MD5) Previous issue date: 2015-04-07"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Symplectic circle actions with isolated fixed points"]}]}],"canonical_facts":{"dc:contributor":["Tolman, Susan","Lerman, Eugene","Kerman, Ely","Leininger, Christopher J."],"dc:creator":["Jang, Donghoon"],"dc:date":["2015-07-22T22:16:27Z","2015-05","2015-04-07","2015-5"],"dc:description":["Consider a symplectic circle action on a closed symplectic manifold $M$ with non-empty isolated fixed points. Associated to each fixed point, there are well-defined non-zero integers, called \\emph{weights}. We prove that the action is Hamiltonian if the sum of an odd number of weights is never equal to the sum of an even number of weights (the weights may be taken at different fixed points). Moreover, we show that if $\\dim M=6$, or if $\\dim M=2n \\leq 10$ and each fixed point has weights $\\{\\pm a_1, \\cdots, \\pm a_n\\}$ for some positive integers $a_i$, the action is Hamiltonian if the sum of three weights is never equal to zero. As applications, we recover the results for semi-free actions, and for certain circle actions on six-dimensional manifolds. Finally, we prove that if there are exactly three fixed points, $M$ is equivariantly symplectomorphic to $\\mathbb{CP}^{2}$.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-07-22 without embargo terms","The student, Donghoon Jang, accepted the attached license on 2015-04-02 at 18:05.","The student, Donghoon Jang, submitted this Dissertation for approval on 2015-04-02 at 18:09.","This Dissertation was approved for publication on 2015-04-07 at 14:20.","DSpace SAF Submission Ingestion Package generated from Vireo submission #7785 on 2015-07-22 at 10:31:25","Made available in DSpace on 2015-07-22T22:16:27Z (GMT). No. of bitstreams: 2 JANG-DISSERTATION-2015.pdf: 496326 bytes, checksum: b3cf126c5fe63cba160877ca04608b19 (MD5) LICENSE.txt: 4210 bytes, checksum: 70bf9842746d3996058376223117fdcf (MD5) Previous issue date: 2015-04-07"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/78347"],"dc:language":["en"],"dc:rights":["Copyright 2015 Donghoon Jang"],"dc:subject":["symplectic circle action","fixed points","Hamiltonian circle action","weights"],"dc:title":["Symplectic circle actions with isolated fixed points"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:11Z"}