2026-09-21T07:04:03Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/125574 2025-02-06 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

application/pdf en text 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 Lefschetz fixed point theory and morse inequalities on stratified pseudomanifolds Jayasinghe, Gayana 2024-07-11 Albin, Pierre Dunfield, Nathan Berwick-Evans, Daniel La Nave, Gabriele Global Analysis Differential Geometry Spectral Theory Singular Spaces Morse Theory Dirac Operators eng 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. 2024-08 Thesis https://hdl.handle.net/2142/125574 Copyright 2024 Gayana Jayasinghe Mathematics Mathematics University of Illinois at Urbana-Champaign Ph.D. Dissertation