Knot Theory: Quandle Module Quivers

In this paper, we introduce an enhancement of the quandle coloring quiver, which is an invariant of oriented knots and links. The opening chapters of this paper are dedicated to providing necessary background knowledge on knot theory before proceeding to the main result. In the primary chapters, we enhance the quandle coloring quiver invariant of oriented knots and links with quandle modules. This results is a two-variable polynomial invariant which specializes to the previous quandle module polynomial invariant as well as to the quandle counting invariant. We provide example computations to show that the enhancement is proper in the sense that it distinguishes knots and links with the same quandle module polynomial