Enhancements of the quandle coloring invariant for knots (Karina Cho, Harvey Mudd College)

Quandles are algebraic structures that play nicely with knots. The multiplicative structure of finite quandles gives us a way to “color” knot diagrams, and the number of such colorings for a given knot and quandle is called the quandle coloring invariant. We strengthen this invariant by examining the relationships between the colorings, which are given by endomorphisms. This can be visualized using a directed graph that we call the quandle coloring quiver. We will show that the quandle coloring quiver is a strict enhancement of the quandle coloring invariant and discuss further enhancements of this invariant that arise from quandle cohomology. This work is a senior thesis project under the advising of Sam Nelson.