Lefschetz fixed point theory and morse inequalities on stratified pseudomanifolds

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Jayasinghe, Gayana

Contributors dc:contributor

• Albin, Pierre
• Dunfield, Nathan
• Berwick-Evans, Daniel
• La Nave, Gabriele

• Global Analysis
• Differential Geometry
• Spectral Theory
• Singular Spaces
• Morse Theory
• Dirac Operators

Statement dc:rights

• Copyright 2024 Gayana Jayasinghe

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/125574

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F125574