2026-09-21T16:51:19Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/124322 2024-09-16 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Dunfield, Nathan M Hirani, Anil N Rasmussen, Jacob Rasmussen, Sarah 2024-05 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms The student, Joseph Malionek, accepted the attached license on 2024-04-17 at 18:26. The student, Joseph Malionek, submitted this Dissertation for approval on 2024-04-17 at 18:49. This Dissertation was approved for publication on 2024-04-18 at 16:42. DSpace SAF Submission Ingestion Package generated from Vireo submission #20468 on 2024-09-16 at 00:35:19 Algorithmic problems in 3-manifold topology and geometry Malionek, Joseph D 2024-04-18 Algorithms Hyperbolic Geometry 3-manifolds 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. Text eng https://hdl.handle.net/2142/124322 Copyright 2024 Joseph Malionek Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics