BYU

Abstract by Jonathon Edevold

Personal Infomation


Presenter's Name

Jonathon Edevold

Degree Level

Undergraduate

Abstract Infomation


Department

Mathematics

Faculty Advisor

Mark Hughes

Title

Representing Knots in Computers

Abstract

A knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions. Knots can be represented using diagrams, which can be transformed via sequences of elementary manipulations called Reidemeister moves. Both knots and Reidemeister moves can be represented using a pair of arrays called extended Gauss code. Extended Gauss code allows for reconstruction of well-defined knots up to topological equivalence. Representing knots this way provides a balance between spatial efficiency and cheap interaction with the knot in an abstract space. Figuring out how to perform Reidemeister moves on Gauss codes provides interesting challenges. Understanding these representations allows us to produce datasets for further studying knots using machine learning techniques.