Honors Program


Document Type


Date of this Version

Winter 3-12-2022


Adams, Gabriel. Exploration of Piccirrillo's Trick on Low Crossing Number Knots. Undergraduate Honors Thesis. University of Nebraska - Lincoln. 2022


You can find the code referenced in the paper here: https://github.com/GabrielAdamsMath/BraidMaker

Copyright Gabriel Adams 2022.


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.

Gabriel Adams Piccirillo Duals LaTeX Final.zip (5559 kB)
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.