Quandle Cohomology Quiver Representations

2024/11/04 by Nelson, Sam · 1 citation
#57K12 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2411.02153

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⊂ H²_Q(x;A), choice of coefficient ring k and set of quandle endomorphisms S⊂ 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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• Virtual Biquandle Cocycle Quiver Representations

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