Honors Program
Document Type
Thesis
Date of this Version
Winter 3-12-2022
Citation
Adams, Gabriel. Exploration of Piccirrillo's Trick on Low Crossing Number Knots. Undergraduate Honors Thesis. University of Nebraska - Lincoln. 2022
Abstract
Piccirillo recently discovered a process that can be applied to an unknotting number one knot to convert it into a different knot called a Piccirillo dual. Piccirillo duals have been shown to have the same n-trace and the same sliceness. However, exploration and knowledge of this process is limited. We were able to generate the Piccirillo duals for several low-crossing number knots. We offer the foundation for and explain how to follow the Piccirillo process and generate Piccirillo duals. This talk assumes little knowledge of knot theory and concisely gives newcomers a clear introduction to get started working with Piccirillo duals.
A zip file with all of the images and LaTeX files.
BraidMaker.py (5 kB)
The braid maker code version at the time of sumbmission.
Included in
Geometry and Topology Commons, Gifted Education Commons, Higher Education Commons, Other Education Commons
Comments
You can find the code referenced in the paper here: https://github.com/GabrielAdamsMath/BraidMaker
Copyright Gabriel Adams 2022.