{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23702"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23702","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Foliations and exotic index theory","abstract":"With regards to certain complete Riemannian manifolds we show that the analytic assembly map is rationally injective by using the exotic index theorem. The foliation exotic index theorem of S. Hurder is an extension of the theorem of G. Yu to the index theory for the foliations. Using the functorial property of the Kasparov KK-product, the foliation exotic index theorem can be recovered via the connecting homomorphism of K-homology theory. In the case of Riemannian foliations on compact manifolds, the corona of the holonomy groupoid is a fiber bundle over the ambient manifold whose fiber is the corona of the universal leaf. By this property, an idea in the work of S. Hurder can be applied to Riemannian foliations on a compact manifold to show that the analytic assembly map for foliations is rationally injective for certain Riemannian foliations.","abstract_html":"With regards to certain complete Riemannian manifolds we show that the analytic assembly map is rationally injective by using the exotic index theorem. The foliation exotic index theorem of S. Hurder is an extension of the theorem of G. Yu to the index theory for the foliations. Using the functorial property of the Kasparov KK-product, the foliation exotic index theorem can be recovered via the connecting homomorphism of K-homology theory. In the case of Riemannian foliations on compact manifolds, the corona of the holonomy groupoid is a fiber bundle over the ambient manifold whose fiber is the corona of the universal leaf. By this property, an idea in the work of S. Hurder can be applied to Riemannian foliations on a compact manifold to show that the analytic assembly map for foliations is rationally injective for certain Riemannian foliations.","abstract_has_math":false,"creators":["Kim, Eunsang"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Kamber, Franz W."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T14:23:54Z","date_published":"2011-05-07T14:23:54Z","updated_at":"2026-07-22T22:25:22Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1996 Kim, Eunsang"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["9780591088021","AAI9702559","(UMI)AAI9702559"],"render_values":[{"text":"9780591088021","href":null,"code":true},{"text":"AAI9702559","href":null,"code":true},{"text":"(UMI)AAI9702559","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23702","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kamber, Franz W."]},{"key":"dc:creator","label":"Author","values":["Kim, Eunsang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:23:54Z","10000-01-01","1996"]},{"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"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1996 Kim, Eunsang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["9780591088021","AAI9702559","(UMI)AAI9702559","http://hdl.handle.net/2142/23702"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["With regards to certain complete Riemannian manifolds we show that the analytic assembly map is rationally injective by using the exotic index theorem. The foliation exotic index theorem of S. Hurder is an extension of the theorem of G. Yu to the index theory for the foliations. Using the functorial property of the Kasparov KK-product, the foliation exotic index theorem can be recovered via the connecting homomorphism of K-homology theory. In the case of Riemannian foliations on compact manifolds, the corona of the holonomy groupoid is a fiber bundle over the ambient manifold whose fiber is the corona of the universal leaf. By this property, an idea in the work of S. Hurder can be applied to Riemannian foliations on a compact manifold to show that the analytic assembly map for foliations is rationally injective for certain Riemannian foliations.","Made available in DSpace on 2011-05-07T14:23:54Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9702559.pdf: 3588820 bytes, checksum: 75035e3aa0371d52a414282331cc3d28 (MD5) Previous issue date: 1996","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:06:16Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:31:48-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Foliations and exotic index theory"]}]}],"canonical_facts":{"dc:contributor":["Kamber, Franz W."],"dc:creator":["Kim, Eunsang"],"dc:date":["2011-05-07T14:23:54Z","10000-01-01","1996"],"dc:description":["With regards to certain complete Riemannian manifolds we show that the analytic assembly map is rationally injective by using the exotic index theorem. The foliation exotic index theorem of S. Hurder is an extension of the theorem of G. Yu to the index theory for the foliations. Using the functorial property of the Kasparov KK-product, the foliation exotic index theorem can be recovered via the connecting homomorphism of K-homology theory. In the case of Riemannian foliations on compact manifolds, the corona of the holonomy groupoid is a fiber bundle over the ambient manifold whose fiber is the corona of the universal leaf. By this property, an idea in the work of S. Hurder can be applied to Riemannian foliations on a compact manifold to show that the analytic assembly map for foliations is rationally injective for certain Riemannian foliations.","Made available in DSpace on 2011-05-07T14:23:54Z (GMT). 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