Non-classicality and quandle difference invariants
摘要
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.
引用
@article{arxiv.math/0601006,
title = {Non-classicality and quandle difference invariants},
author = {Natasha Harrell and Sam Nelson},
journal= {arXiv preprint arXiv:math/0601006},
year = {2007}
}
备注
10 pages. Version 3: Changes made as suggested by referee. To appear in Topology Proceedings