Non-classicality and quandle difference invariants
| dc.creator | Harrell, Natasha | |
| dc.creator | Nelson, Sam | |
| dc.date | 2006-01-02 | |
| dc.date | 2006-06-05 | |
| dc.date.accessioned | 2026-07-07T07:45:01Z | |
| dc.date.available | 2026-07-07T07:45:01Z | |
| dc.description | 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. | |
| dc.description | 10 pages. Version 3: Changes made as suggested by referee. To appear in Topology Proceedings | |
| dc.identifier | https://arxiv.org/abs/math/0601006 | |
| dc.identifier | http://arxiv.org/abs/math/0601006 | |
| dc.identifier | Topology Proceedings 30 (2006) 251-263. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123406 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25, 57M27 | |
| dc.title | Non-classicality and quandle difference invariants | |
| dc.type | text |