Quandle Action Quivers

Abstract

Quandle Coloring Quivers are directed graph-valued invariants of classical and virtual knots and links associated to finite quandles. Quandle action quivers are subquivers of the full quandle coloring quiver associated to quandle actions by elements of the coloring quandle. These quivers provide a categorification of the quandle counting invariant associated to each element of the quandle. We obtain new polynomial invariants called quandle action polynomials from these quivers as decategorifications.