Researcher ORCID Identifier
Open Access Senior Thesis
Bachelor of Science
© 2022 Ryan M Martinez
In this thesis we first give an introduction to knots, knot diagrams, and algebraic structures defined on them accessible to anyone with knowledge of very basic abstract algebra and topology. Of particular interest in this thesis is the quandle which "colors" knot diagrams. Usually, quandles are only used to color knot diagrams in the plane or on a sphere, so this thesis extends quandles to knot diagrams on any surface and begins to classify the fundamental quandles of knot diagrams on the torus.
This thesis also breifly looks into Niebrzydowski Tribrackets which are a different algebraic structure which, in future work, may have interesting behavior on knot diagrams in arbitrary surfaces.
Martinez, Ryan, "Algebraic Invariants of Knot Diagrams on Surfaces" (2022). HMC Senior Theses. 260.