{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71209"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71209","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Generic Reductions of an Integrable G-Structure and an Infinitesimal Version of Cartan-Sternberg Reduction","abstract":"Given an integrable G-structure P and a closed subgroup H of G, we assign to each H-reduction of P a singular set in the base manifold. Our first main result is that generically, this singular set is a finite disjoint union of submanifolds (our theorem generalizes an unpublished result of L. Lipskie). The group can often be reduced even further off this singular set by a method of Cartan and Sternberg.","abstract_html":"Given an integrable G-structure P and a closed subgroup H of G, we assign to each H-reduction of P a singular set in the base manifold. Our first main result is that generically, this singular set is a finite disjoint union of submanifolds (our theorem generalizes an unpublished result of L. Lipskie). The group can often be reduced even further off this singular set by a method of Cartan and Sternberg.","abstract_has_math":false,"creators":["Thomas, Mark Allen"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T06:18:04Z","date_published":"2014-12-16T06:18:04Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8324657"],"render_values":[{"text":"(UMI)AAI8324657","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71209","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Thomas, Mark Allen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:04Z","10000-01-01","1983"]},{"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":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71209","(UMI)AAI8324657"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Given an integrable G-structure P and a closed subgroup H of G, we assign to each H-reduction of P a singular set in the base manifold. Our first main result is that generically, this singular set is a finite disjoint union of submanifolds (our theorem generalizes an unpublished result of L. Lipskie). The group can often be reduced even further off this singular set by a method of Cartan and Sternberg.","Motivated by the desire to obtain further transversality results concerning the Cartan-Sternberg reduction method, we give the beginning of an "infinitesimal" theory of Cartan-Sternberg reduction. Specifically, our second main result is that the method is well-defined on a certain set of jets of G-structures. Our third main result is that the reduction mapping thus obtained is smooth whenever the set of reducible jets is a manifold. (We conjecture that in general, this set is indeed a manifold).","Made available in DSpace on 2014-12-16T06:18:04Z (GMT). No. of bitstreams: 1 8324657.pdf: 2582771 bytes, checksum: 71cd0e404207758ff28c8a00a744dba0 (MD5) Previous issue date: 1983","Embargo set by: Seth Robbins for item 71375 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","92 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983."]},{"key":"dc:title","label":"Title","values":["Generic Reductions of an Integrable G-Structure and an Infinitesimal Version of Cartan-Sternberg Reduction"]}]}],"canonical_facts":{"dc:creator":["Thomas, Mark Allen"],"dc:date":["2014-12-16T06:18:04Z","10000-01-01","1983"],"dc:description":["Given an integrable G-structure P and a closed subgroup H of G, we assign to each H-reduction of P a singular set in the base manifold. Our first main result is that generically, this singular set is a finite disjoint union of submanifolds (our theorem generalizes an unpublished result of L. Lipskie). The group can often be reduced even further off this singular set by a method of Cartan and Sternberg.","Motivated by the desire to obtain further transversality results concerning the Cartan-Sternberg reduction method, we give the beginning of an "infinitesimal" theory of Cartan-Sternberg reduction. Specifically, our second main result is that the method is well-defined on a certain set of jets of G-structures. Our third main result is that the reduction mapping thus obtained is smooth whenever the set of reducible jets is a manifold. (We conjecture that in general, this set is indeed a manifold).","Made available in DSpace on 2014-12-16T06:18:04Z (GMT). No. of bitstreams: 1 8324657.pdf: 2582771 bytes, checksum: 71cd0e404207758ff28c8a00a744dba0 (MD5) Previous issue date: 1983","Embargo set by: Seth Robbins for item 71375 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","92 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983."],"dc:identifier":["http://hdl.handle.net/2142/71209","(UMI)AAI8324657"],"dc:subject":["Mathematics"],"dc:title":["Generic Reductions of an Integrable G-Structure and an Infinitesimal Version of Cartan-Sternberg Reduction"],"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":"2026-07-22T22:26:04Z"}