{"id":{"repo_id":"uwo","oai_identifier":"oai:uwo.scholaris.ca:20.500.14721/21329"},"canonical_url":"https://search.dev.ndltd.org/etd/uwo/oai:uwo.scholaris.ca:20.500.14721/21329","repository":{"repo_id":"uwo","name":"Western University","base_url":"https://uwo.scholaris.ca/server/oai/request"},"display":{"title":"Generalizations Of The Segal Conjecture","abstract":"The main result of this thesis may be described in the following manner: Let G be a finite group and let {dollar}pi{dollar} be a compact Lie group. Define A(G,{dollar}pi{dollar}) to be the free abelian group generated by equivalence classes of subhomomorphisms (G {dollar}supset{dollar} H {dollar}{lcub}buildrelrhooverlongrightarrow{rcub} pi){dollar}. A(G,{dollar}pi{dollar}) is a module over the Burnside ring A(G). Define a map to stable homotopy which sends this subhomomorphism to the stable map BG{dollar}sb+{dollar} {dollar}{lcub}buildrelrm transferoverlongrightarrow{rcub}{dollar} BH{dollar}sb+{dollar} {dollar}{lcub}buildrelrm Brhosb+overlongrightarrow{rcub}{dollar} B{dollar}pisb+{dollar}. This recipe defines a map {dollar}Psi{dollar}: A(G,{dollar}pi)sbsp{lcub}rm IA(G){rcub}{lcub}{rcub}{dollar} {dollar}to{dollar} {dollar}{lcub}{dollar}BG{dollar}sb+{dollar}, B{dollar}pisb+{rcub}{dollar}. Our main result states that {dollar}Psi{dollar} is an isomorphism. This generalises Carlsson's proof of the Segal conjecture.","abstract_html":"The main result of this thesis may be described in the following manner: Let G be a finite group and let {dollar}pi{dollar} be a compact Lie group. Define A(G,{dollar}pi{dollar}) to be the free abelian group generated by equivalence classes of subhomomorphisms (G {dollar}supset{dollar} H {dollar}{lcub}buildrelrhooverlongrightarrow{rcub} pi){dollar}. A(G,{dollar}pi{dollar}) is a module over the Burnside ring A(G). Define a map to stable homotopy which sends this subhomomorphism to the stable map BG{dollar}sb+{dollar} {dollar}{lcub}buildrelrm transferoverlongrightarrow{rcub}{dollar} BH{dollar}sb+{dollar} {dollar}{lcub}buildrelrm Brhosb+overlongrightarrow{rcub}{dollar} B{dollar}pisb+{dollar}. This recipe defines a map {dollar}Psi{dollar}: A(G,{dollar}pi)sbsp{lcub}rm IA(G){rcub}{lcub}{rcub}{dollar} {dollar}to{dollar} {dollar}{lcub}{dollar}BG{dollar}sb+{dollar}, B{dollar}pisb+{rcub}{dollar}. Our main result states that {dollar}Psi{dollar} is an isomorphism. This generalises Carlsson's proof of the Segal conjecture.","abstract_has_math":false,"creators":["Zelewski, Piotr Mavian"],"institution":null,"degree_name":"Ph D","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1988,"date_issued":"1988-01-01","date_published":"1988-01-01","updated_at":"2026-07-27T21:55:58Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/20.500.14721/21329","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Zelewski, Piotr Mavian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-06-25T19:47:57Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-06-25T19:47:57Z"]},{"key":"dc:date.issued","label":"Date","values":["1988-01-01"]},{"key":"dc:type","label":"Dc Type","values":["thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph D"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/20.500.14721/21329"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The main result of this thesis may be described in the following manner: Let G be a finite group and let {dollar}pi{dollar} be a compact Lie group. Define A(G,{dollar}pi{dollar}) to be the free abelian group generated by equivalence classes of subhomomorphisms (G {dollar}supset{dollar} H {dollar}{lcub}buildrelrhooverlongrightarrow{rcub} pi){dollar}. A(G,{dollar}pi{dollar}) is a module over the Burnside ring A(G). Define a map to stable homotopy which sends this subhomomorphism to the stable map BG{dollar}sb+{dollar} {dollar}{lcub}buildrelrm transferoverlongrightarrow{rcub}{dollar} BH{dollar}sb+{dollar} {dollar}{lcub}buildrelrm Brhosb+overlongrightarrow{rcub}{dollar} B{dollar}pisb+{dollar}. This recipe defines a map {dollar}Psi{dollar}: A(G,{dollar}pi)sbsp{lcub}rm IA(G){rcub}{lcub}{rcub}{dollar} {dollar}to{dollar} {dollar}{lcub}{dollar}BG{dollar}sb+{dollar}, B{dollar}pisb+{rcub}{dollar}. Our main result states that {dollar}Psi{dollar} is an isomorphism. This generalises Carlsson's proof of the Segal conjecture."]},{"key":"dc:title","label":"Title","values":["Generalizations Of The Segal Conjecture"]}]}],"canonical_facts":{"dc:creator":["Zelewski, Piotr Mavian"],"dc:date.accessioned":["2025-06-25T19:47:57Z"],"dc:date.available":["2025-06-25T19:47:57Z"],"dc:date.issued":["1988-01-01"],"dc:description.abstract":["The main result of this thesis may be described in the following manner: Let G be a finite group and let {dollar}pi{dollar} be a compact Lie group. Define A(G,{dollar}pi{dollar}) to be the free abelian group generated by equivalence classes of subhomomorphisms (G {dollar}supset{dollar} H {dollar}{lcub}buildrelrhooverlongrightarrow{rcub} pi){dollar}. A(G,{dollar}pi{dollar}) is a module over the Burnside ring A(G). Define a map to stable homotopy which sends this subhomomorphism to the stable map BG{dollar}sb+{dollar} {dollar}{lcub}buildrelrm transferoverlongrightarrow{rcub}{dollar} BH{dollar}sb+{dollar} {dollar}{lcub}buildrelrm Brhosb+overlongrightarrow{rcub}{dollar} B{dollar}pisb+{dollar}. This recipe defines a map {dollar}Psi{dollar}: A(G,{dollar}pi)sbsp{lcub}rm IA(G){rcub}{lcub}{rcub}{dollar} {dollar}to{dollar} {dollar}{lcub}{dollar}BG{dollar}sb+{dollar}, B{dollar}pisb+{rcub}{dollar}. Our main result states that {dollar}Psi{dollar} is an isomorphism. This generalises Carlsson's proof of the Segal conjecture."],"dc:identifier.uri":["https://hdl.handle.net/20.500.14721/21329"],"dc:subject":["Mathematics"],"dc:title":["Generalizations Of The Segal Conjecture"],"dc:type":["thesis"],"thesis:degree_name":["Ph D"]},"updated_at":"2026-07-27T21:55:58Z"}