Mathematics – Geometric Topology
Scientific paper
2006-01-02
Topology Proceedings 30 (2006) 251-263.
Mathematics
Geometric Topology
10 pages. Version 3: Changes made as suggested by referee. To appear in Topology Proceedings
Scientific paper
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 intersticed Gauss codes with 3 and 4 crossings. For non-evenly intersticed Gauss codes with 4 crossings, the difference invariant detects non-classicality in 86% of codes which have non-trivial upper or lower counting invariant values.
Harrell Natasha
Nelson Sam
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