• Corpus ID: 117958162

Non-classicality and quandle difference invariants

@article{Harrell2006NonclassicalityAQ,
  title={Non-classicality and quandle difference invariants},
  author={Natasha Harrell and Sam Nelson},
  journal={arXiv: Geometric Topology},
  year={2006}
}
  • N. Harrell, Sam Nelson
  • Published 2 January 2006
  • Computer Science, Mathematics
  • arXiv: Geometric Topology
Non-classical virtual knots may have non-isomorphic upper and lower quandles. We exploit this property to define the quandle difference invariant, which can detect non-classicality by comparing the numbers of homomorphisms into a finite quandle from a virtual knot's upper and lower quandles. The invariants for small-order finite quandles detect non-classicality in several interesting virtual knots. We compute the difference invariant with the six smallest connected quandles for all non-evenly… 
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