Date of Award
Master of Science
Math and Computer Science
There are many papers that introduce the relationship between knots and quandles which are written tersely and focus mainly on applications or implications. Here, we will take time to explain in depth how to derive quandles from oriented knots. Starting with an rigorous introduction to what a knot is and what a quandle is, we will also define the Fundamental Quandle of a knot and the relationship between colorings of a knot and the homomorphisms from an arbitrary quandle to a Fundamental Quandle. Then using this foundation, we will examine two sets of knots that produce quandles that contain subquandles and the set of quandles created by non-oriented knots.
Haskell, Jason, "Quandles that are Knot Quandles" (2022). All NMU Master's Theses. 698.