Date of Creation
5-2025
Document Type
Departmental Honors Thesis
Department
Mathematics
First Advisor
Neranga Fernando
Abstract
We explore the mathematical theory of knots through the lens of algebraic structures known as kei and quandles. We begin by introducing classical knot invariants and then study the fundamental kei of a knot as a tool for distinguishing knot types. We generalize this approach using various kinds of quandles, including Alexander and dihedral quandles, and investigate their associated polynomial invariants. We also examine the connection between quandles and group theory, as well as their algebraic representations in quandle rings. Moreover, we analyze idempotent elements in quandle rings over finite fields, providing both general results and specific examples.
Recommended Citation
Wu, Zhaoqi, "A Study of Knots and Quandles" (2025). Math and Computer Science Honors Theses. 64.
https://crossworks.holycross.edu/math_honor/64