Quandle Cohomology Quiver Representations

Sam Nelson

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arXiv · 2411.02153

Quandle Cohomology Quiver Representations

Sam Nelson

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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.

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Sam Nelson. 2024-11-04. Quandle Cohomology Quiver Representations. https://arxiv.org/abs/2411.02153

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