Reidemeister Torsion and the Classification of Three-Dimentional Lens Spaces
Date of Award
2011
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
Mullins, David
Keywords
Math, Lens Spaces, Topological Invariants
Area of Concentration
Mathematics
Abstract
Topological invariants are crucial tools for solving classification problems in algebraic topology. Here, we state the definition of invariance and proceed to develop the fundamental group, homology of chain complexes and Reidemeister torsion in the context of classifying three-dimensional lens spaces. We will show that only the Reidemeister torsion is sufficient for classifying lens spaces up to homeomorphism. While this is a classical result, we develop most of the necessary theory and attempt to make the material accessible to advanced undergraduates.
Recommended Citation
Raoux, Katherine, "Reidemeister Torsion and the Classification of Three-Dimentional Lens Spaces" (2011). Theses & ETDs. 4446.
https://digitalcommons.ncf.edu/theses_etds/4446