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Algorithmic problems in 3-manifold topology and geometry
Malionek, Joseph D
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https://hdl.handle.net/2142/124322
Description
- Title
- Algorithmic problems in 3-manifold topology and geometry
- Author(s)
- Malionek, Joseph D
- Issue Date
- 2024-04-18
- Director of Research (if dissertation) or Advisor (if thesis)
- Dunfield, Nathan M
- Doctoral Committee Chair(s)
- Hirani, Anil N
- Committee Member(s)
- Rasmussen, Jacob
- Rasmussen, Sarah
- Department of Study
- Mathematics
- Discipline
- Mathematics
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Keyword(s)
- algorithms
- hyperbolic geometry
- 3-manifolds
- Abstract
- This is a study of two algorithmic problems in low-dimensional topology in geometry. The first chapter presents some results on twisted Alexander polynomials. I show that for torsion polynomials twisted by 2-dimensional representations, the coefficients are determined solely by the traces of the matrices in the representation. The second chapter details joint work with Brannon Basilio and Chaeryn Lee concerning totally geodesic surfaces. We produce an algorithm which determines when a hyperbolic 3-manifold contains a totally geodesic surface. For both of these projects, practical algorithms were implemented and extensive examples were calculated.
- Graduation Semester
- 2024-05
- Type of Resource
- Thesis
- Handle URL
- https://hdl.handle.net/2142/124322
- Copyright and License Information
- Copyright 2024 Joseph Malionek
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Graduate Dissertations and Theses at Illinois PRIMARY
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