{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86774"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86774","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Complexity One Hamiltonian SU(2) and SO(3) Actions","abstract":"Main Theorem. (Local Uniqueness over 0). Let G be SU(2) or SO(3). Let (M, o, phi), and (M', o', phi ') be six dimensional compact connected Hamiltonian G-manifolds such that 0 ∈ phi(M) = phi '(M'). There exists an invariant neighborhood V of 0 in g* over which the Hamiltonian G-manifolds are isomorphic if and only if (1) their Duistermaat-Heckman functions coincide; (2) their isotropy data and genus at 0 are the same; (3) if the zero fibers are tall with principal isotropy group S1, the first Stiefel-Whitney classes of phi-1(0) and phi '-1(0) in H1( Mreg0;Z2 ) and H1 ( M'reg0;Z2 ) are equal (under a proper identification of the reduced spaces at 0).","abstract_html":"Main Theorem. (Local Uniqueness over 0). Let G be SU(2) or SO(3). Let (M, o, phi), and (M', o', phi ') be six dimensional compact connected Hamiltonian G-manifolds such that 0 ∈ phi(M) = phi '(M'). There exists an invariant neighborhood V of 0 in g* over which the Hamiltonian G-manifolds are isomorphic if and only if (1) their Duistermaat-Heckman functions coincide; (2) their isotropy data and genus at 0 are the same; (3) if the zero fibers are tall with principal isotropy group S1, the first Stiefel-Whitney classes of phi-1(0) and phi '-1(0) in H1( Mreg0;Z2 ) and H1 ( M'reg0;Z2 ) are equal (under a proper identification of the reduced spaces at 0).","abstract_has_math":false,"creators":["Chiang, River"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Susan Tolman"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:28Z","date_published":"2015-09-28T15:19:28Z","updated_at":"2026-07-22T22:26:27Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3017043"],"render_values":[{"text":"(MiAaPQ)AAI3017043","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86774","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Susan Tolman"]},{"key":"dc:creator","label":"Author","values":["Chiang, River"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:28Z","10000-01-01","2001"]},{"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":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86774","(MiAaPQ)AAI3017043"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Main Theorem. (Local Uniqueness over 0). Let G be SU(2) or SO(3). Let (M, o, phi), and (M', o', phi ') be six dimensional compact connected Hamiltonian G-manifolds such that 0 ∈ phi(M) = phi '(M'). There exists an invariant neighborhood V of 0 in g* over which the Hamiltonian G-manifolds are isomorphic if and only if (1) their Duistermaat-Heckman functions coincide; (2) their isotropy data and genus at 0 are the same; (3) if the zero fibers are tall with principal isotropy group S1, the first Stiefel-Whitney classes of phi-1(0) and phi '-1(0) in H1( Mreg0;Z2 ) and H1 ( M'reg0;Z2 ) are equal (under a proper identification of the reduced spaces at 0).","Made available in DSpace on 2015-09-28T15:19:28Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3017043.pdf: 2323247 bytes, checksum: 3a84e07e420b60eba8222074de7c59ab (MD5) Previous issue date: 2001","Embargo set by: Seth Robbins for item 88055 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","46 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001."]},{"key":"dc:title","label":"Title","values":["Complexity One Hamiltonian SU(2) and SO(3) Actions"]}]}],"canonical_facts":{"dc:contributor":["Susan Tolman"],"dc:creator":["Chiang, River"],"dc:date":["2015-09-28T15:19:28Z","10000-01-01","2001"],"dc:description":["Main Theorem. (Local Uniqueness over 0). Let G be SU(2) or SO(3). Let (M, o, phi), and (M', o', phi ') be six dimensional compact connected Hamiltonian G-manifolds such that 0 ∈ phi(M) = phi '(M'). There exists an invariant neighborhood V of 0 in g* over which the Hamiltonian G-manifolds are isomorphic if and only if (1) their Duistermaat-Heckman functions coincide; (2) their isotropy data and genus at 0 are the same; (3) if the zero fibers are tall with principal isotropy group S1, the first Stiefel-Whitney classes of phi-1(0) and phi '-1(0) in H1( Mreg0;Z2 ) and H1 ( M'reg0;Z2 ) are equal (under a proper identification of the reduced spaces at 0).","Made available in DSpace on 2015-09-28T15:19:28Z (GMT). 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