{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71267"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71267","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Minimal Models and Riemannian Foliations","abstract":"In this work, we consider minimal models of Riemannian foliations on connected, simply-connected manifolds following Lehmann. We show that if the minimal model has an underlying rational form of finite type, then it can be realized in rational homotopy by a fibration of finite CW complexes. As a consequence, based on results of Gottlieb and Chern-Hirzebruch-Serre, a signature product formula is obtained.","abstract_html":"In this work, we consider minimal models of Riemannian foliations on connected, simply-connected manifolds following Lehmann. We show that if the minimal model has an underlying rational form of finite type, then it can be realized in rational homotopy by a fibration of finite CW complexes. As a consequence, based on results of Gottlieb and Chern-Hirzebruch-Serre, a signature product formula is obtained.","abstract_has_math":false,"creators":["Pang, Peter Yu-Hin"],"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":"2014-12-16T06:18:22Z","date_published":"2014-12-16T06:18:22Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8823223"],"render_values":[{"text":"(UMI)AAI8823223","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71267","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Pang, Peter Yu-Hin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:22Z","10000-01-01","1988"]},{"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/2142/71267","(UMI)AAI8823223"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this work, we consider minimal models of Riemannian foliations on connected, simply-connected manifolds following Lehmann. We show that if the minimal model has an underlying rational form of finite type, then it can be realized in rational homotopy by a fibration of finite CW complexes. As a consequence, based on results of Gottlieb and Chern-Hirzebruch-Serre, a signature product formula is obtained.","In the second part, inspired by Hurder, basic dual homotopy invariants of Riemannian foliations are defined using minimal models. Existence and vanishing theorems are proved for these invariants.","Made available in DSpace on 2014-12-16T06:18:22Z (GMT). No. of bitstreams: 1 8823223.pdf: 5287135 bytes, checksum: b5fbae28fcdb81c395b276f4ceb260f7 (MD5) Previous issue date: 1988","Embargo set by: Seth Robbins for item 71433 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","148 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988."]},{"key":"dc:title","label":"Title","values":["Minimal Models and Riemannian Foliations"]}]}],"canonical_facts":{"dc:creator":["Pang, Peter Yu-Hin"],"dc:date":["2014-12-16T06:18:22Z","10000-01-01","1988"],"dc:description":["In this work, we consider minimal models of Riemannian foliations on connected, simply-connected manifolds following Lehmann. We show that if the minimal model has an underlying rational form of finite type, then it can be realized in rational homotopy by a fibration of finite CW complexes. As a consequence, based on results of Gottlieb and Chern-Hirzebruch-Serre, a signature product formula is obtained.","In the second part, inspired by Hurder, basic dual homotopy invariants of Riemannian foliations are defined using minimal models. Existence and vanishing theorems are proved for these invariants.","Made available in DSpace on 2014-12-16T06:18:22Z (GMT). No. of bitstreams: 1 8823223.pdf: 5287135 bytes, checksum: b5fbae28fcdb81c395b276f4ceb260f7 (MD5) Previous issue date: 1988","Embargo set by: Seth Robbins for item 71433 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","148 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988."],"dc:identifier":["http://hdl.handle.net/2142/71267","(UMI)AAI8823223"],"dc:subject":["Mathematics"],"dc:title":["Minimal Models and Riemannian Foliations"],"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"}