# 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} }

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…

## One Citation

The column group and its link invariants

- Mathematics
- 2009

The column group is a subgroup of the symmetric group on the elements of a finite blackboard birack generated by the column permutations in the birack matrix. We use subgroups of the column group…

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