University of Illinois Urbana-Champaign

Lefschetz fixed point theory and morse inequalities on stratified pseudomanifolds

Jayasinghe, Gayana

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

Description

Title
Lefschetz fixed point theory and morse inequalities on stratified pseudomanifolds
Author(s)
Jayasinghe, Gayana
Issue Date
2024-07-11
Director of Research (if dissertation) or Advisor (if thesis)
Albin, Pierre
Doctoral Committee Chair(s)
Dunfield, Nathan
Committee Member(s)
  • Berwick-Evans, Daniel
  • La Nave, Gabriele
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Global Analysis
  • Differential geometry
  • Spectral theory
  • Singular spaces
  • Morse theory
  • Dirac operators
Abstract
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.
Graduation Semester
2024-08
Type of Resource
Thesis
Handle URL
https://hdl.handle.net/2142/125574
Copyright and License Information
Copyright 2024 Gayana Jayasinghe

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