Quandle Cohomology Quiver Representations

Abstract

We define a family of quiver representation-valued invariants of oriented classical and virtual knots and links associated to a choice of finite quandle $X$, abelian group $A$, set of quandle 2-cocycles $C\subset H^2_Q(x;A)$, choice of coefficient ring $k$ and set of quandle endomorphisms $S\subset \mathrm{Hom}(X,X)$. From this representation we define four new polynomial (or ``polynomial'' depending on $A$) invariants. We generalize to the case of biquandles and compute some examples.