English

Quandle Cohomology Quiver Representations

Geometric Topology 2024-12-24 v2 Quantum Algebra

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 XX, abelian group AA, set of quandle 2-cocycles CHQ2(x;A)C\subset H^2_Q(x;A), choice of coefficient ring kk and set of quandle endomorphisms SHom(X,X)S\subset \mathrm{Hom}(X,X). From this representation we define four new polynomial (or ``polynomial'' depending on AA) invariants. We generalize to the case of biquandles and compute some examples.

Keywords

Cite

@article{arxiv.2411.02153,
  title  = {Quandle Cohomology Quiver Representations},
  author = {Sam Nelson},
  journal= {arXiv preprint arXiv:2411.02153},
  year   = {2024}
}

Comments

15 pages. Version 2 includes expanded proofs and typo corrections