Senior Project Advisor
Jeffrey Meier
Document Type
Project
Publication Date
Winter 2025
Keywords
mathematics, topology, knot theory
Abstract
This project has endeavored to produce a knotted RP2 with order-4 meridians by developing randomized algorithms capable of constructing and analyzing knotted surfaces. We build off of the work of Jack Maxon and Astrea Rollins to generate trivial tangles and tri-plane diagrams and to compute the surface types and surface link groups of resulting tri-plane diagrams. In total, we generate nearly 1.5 million triples of tangles, yielding almost 200,000 valid tri-plane diagrams. Ultimately, very few of these diagrams are non-trivially knotted, as detected by the fundamental group, and our search does not produce the desired surface. However, our exploration provides ample data and new insights for the future computational study of knotted surfaces.
Department
Mathematics
Recommended Citation
Ward, Mayla, "Randomized Computational Search for Topological Unicorns" (2025). WWU Honors College Senior Projects. 912.
https://cedar.wwu.edu/wwu_honors/912
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf