Graduation Year
2019
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Sam Nelson
Reader 2
Francis Edward Su
Rights Information
2019 Karina E Cho
Abstract
Quandles, which are algebraic structures related to knots, can be used to color knot diagrams, and the number of these colorings is called the quandle coloring invariant. We strengthen the quandle coloring invariant by considering a graph structure on the space of quandle colorings of a knot, and we call our graph the quandle coloring quiver. This structure is a categorification of the quandle coloring invariant. Then, we strengthen the quiver by decorating it with Boltzmann weights. Explicit examples of links that show that our enhancements are proper are provided, as well as background information in quandle theory.
Recommended Citation
Cho, Karina Elle, "Enhancing the Quandle Coloring Invariant for Knots and Links" (2019). HMC Senior Theses. 228.
https://scholarship.claremont.edu/hmc_theses/228
