{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/125574"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/125574","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Lefschetz fixed point theory and morse inequalities on stratified pseudomanifolds","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. 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The submission was exported from vireo on 2025-02-04 without embargo terms","The student, Gayana Jayasinghe, accepted the attached license on 2024-07-06 at 12:55.","The student, Gayana Jayasinghe, submitted this Dissertation for approval on 2024-07-06 at 13:06.","This Dissertation was approved for publication on 2024-07-11 at 07:31.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20970 on 2025-02-04 at 21:04:19","In this dissertation, we develop a new framework to understand Lefschetz fixed point theorems and Morse inequalities for elliptic complexes on stratified pseudomanifolds. We prove generalizations of the Atiyah-Bott-Lefschetz fixed point theorem and construct Witten instanton complexes for various operators on such spaces, comparing and contrasting versions for different elliptic complexes and versions for other cohomology theories, and studying applications in mathematics and physics."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Lefschetz fixed point theory and morse inequalities on stratified pseudomanifolds"]}]}],"canonical_facts":{"dc:contributor":["Albin, Pierre","Dunfield, Nathan","Berwick-Evans, Daniel","La Nave, Gabriele"],"dc:creator":["Jayasinghe, Gayana"],"dc:date":["2024-07-11","2024-08"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms","The student, Gayana Jayasinghe, accepted the attached license on 2024-07-06 at 12:55.","The student, Gayana Jayasinghe, submitted this Dissertation for approval on 2024-07-06 at 13:06.","This Dissertation was approved for publication on 2024-07-11 at 07:31.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20970 on 2025-02-04 at 21:04:19","In this dissertation, we develop a new framework to understand Lefschetz fixed point theorems and Morse inequalities for elliptic complexes on stratified pseudomanifolds. We prove generalizations of the Atiyah-Bott-Lefschetz fixed point theorem and construct Witten instanton complexes for various operators on such spaces, comparing and contrasting versions for different elliptic complexes and versions for other cohomology theories, and studying applications in mathematics and physics."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/125574"],"dc:language":["en","eng"],"dc:rights":["Copyright 2024 Gayana Jayasinghe"],"dc:subject":["Global Analysis","Differential Geometry","Spectral Theory","Singular Spaces","Morse Theory","Dirac Operators"],"dc:title":["Lefschetz fixed point theory and morse inequalities on stratified pseudomanifolds"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:02Z"}