{"id":{"repo_id":"oregon","oai_identifier":"oai:scholarsbank.uoregon.edu:1794/19241"},"canonical_url":"https://search.dev.ndltd.org/etd/oregon/oai:scholarsbank.uoregon.edu:1794/19241","repository":{"repo_id":"oregon","name":"University of Oregon","base_url":"https://scholarsbank.uoregon.edu/server/oai/request"},"display":{"title":"Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds","abstract":"Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n-1)-connected, (4n+1)-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the action of the diffeomorphism group of a manifold M on the linking form associated to the homology groups of M. In order to study this action we construct a geometric model for the linking form using the intersections of embedded and immersed Z/k-manifolds. In addition to our main homological stability theorem, we prove several results regarding disjunction for embeddings and immersions of Z/k-manifolds that could be of independent interest.","abstract_html":"Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n-1)-connected, (4n+1)-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the action of the diffeomorphism group of a manifold M on the linking form associated to the homology groups of M. In order to study this action we construct a geometric model for the linking form using the intersections of embedded and immersed Z/k-manifolds. In addition to our main homological stability theorem, we prove several results regarding disjunction for embeddings and immersions of Z/k-manifolds that could be of independent interest.","abstract_has_math":false,"creators":["Perlmutter, Nathan"],"institution":"University of Oregon","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":"Department of Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Botvinnik, Boris"],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-08-18","date_published":"2015-08-18","updated_at":"2026-08-21T16:47:20Z","subjects":["Algebraic topology","Diffeomorphism groups","Differential topology","Singularity Theory","Surgery Theory"],"languages":["en_US"],"rights":["All Rights Reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1794/19241","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://scholarsbank.uoregon.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Ascholarsbank.uoregon.edu%3A1794%2F19241","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Botvinnik, Boris"]},{"key":"dc:creator","label":"Author","values":["Perlmutter, Nathan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-08-18T23:01:18Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-08-18T23:01:18Z"]},{"key":"dc:date.issued","label":"Date","values":["2015-08-18"]},{"key":"dc:publisher","label":"Institution","values":["University of Oregon"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Oregon"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic topology","Diffeomorphism groups","Differential topology","Singularity Theory","Surgery Theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["All Rights Reserved."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1794/19241"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n-1)-connected, (4n+1)-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the action of the diffeomorphism group of a manifold M on the linking form associated to the homology groups of M. In order to study this action we construct a geometric model for the linking form using the intersections of embedded and immersed Z/k-manifolds. In addition to our main homological stability theorem, we prove several results regarding disjunction for embeddings and immersions of Z/k-manifolds that could be of independent interest."]},{"key":"dc:title","label":"Title","values":["Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds"]}]}],"canonical_facts":{"dc:contributor.advisor":["Botvinnik, Boris"],"dc:creator":["Perlmutter, Nathan"],"dc:date.accessioned":["2015-08-18T23:01:18Z"],"dc:date.available":["2015-08-18T23:01:18Z"],"dc:date.issued":["2015-08-18"],"dc:description.abstract":["Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n-1)-connected, (4n+1)-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the action of the diffeomorphism group of a manifold M on the linking form associated to the homology groups of M. In order to study this action we construct a geometric model for the linking form using the intersections of embedded and immersed Z/k-manifolds. In addition to our main homological stability theorem, we prove several results regarding disjunction for embeddings and immersions of Z/k-manifolds that could be of independent interest."],"dc:identifier.uri":["https://hdl.handle.net/1794/19241"],"dc:language.iso":["en_US"],"dc:publisher":["University of Oregon"],"dc:rights":["All Rights Reserved."],"dc:subject":["Algebraic topology","Diffeomorphism groups","Differential topology","Singularity Theory","Surgery Theory"],"dc:title":["Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Department of Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Oregon"]},"updated_at":"2026-08-21T16:47:20Z"}