Quandle coloring quivers of links using dihedral quandles (2004.12437v1)

Abstract: K. Cho and S. Nelson introduced the notion of a quandle coloring quiver, which is a quiver-valued link invariant, and a quandle cocycle quiver which is an enhancement of the quandle coloring quiver by assigning to each vertex a weight computed using a quandle 2-cocycle. In this paper, we study quandle coloring quivers using dihedral quandles and introduce the notions of a shadow quandle coloring quiver and a shadow quandle cocycle quiver, which are shadow versions of the quandle coloring quiver and the quandle cocycle quiver. We show that, when we use a dihedral quandle of prime order, the quandle coloring quivers are equivalent to the quandle coloring numbers and when we use a dihedral quandle of prime order and Mochizuki's 3-cocycle, the shadow quandle cocycle quivers are equivalent to the shadow quandle cocycle invariants.