Virtual knots undetected by 1 and 2-strand bracket polynomials
| dc.creator | Dye, H. A. | |
| dc.date | 2004-02-18 | |
| dc.date.accessioned | 2026-07-07T05:05:35Z | |
| dc.date.available | 2026-07-07T05:05:35Z | |
| dc.description | Kishino's knot is not detected by the fundamental group or the bracket polynomial; these invariants cannot differentiate between Kishino's knot and the unknot. However, we can show that Kishino's knot is not equivalent to unknot by applying either the 3-strand bracket polynomial or the surface bracket polynomial. In this paper, we construct two non-trivial virtual knot diagrams, $ K_D $ and $ K_m $, that are not not detected by the bracket polynomial or the 2-strand bracket polynomial. From these diagrams, we construct two infinite families of non-classical virtual knot diagrams that are not detected by the bracket polynomial. Additionally, we note these virtual knot diagrams are trivial as flats. | |
| dc.description | 22 pages, 24 figures | |
| dc.identifier | https://arxiv.org/abs/math/0402308 | |
| dc.identifier | http://arxiv.org/abs/math/0402308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70215 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M27 | |
| dc.title | Virtual knots undetected by 1 and 2-strand bracket polynomials | |
| dc.type | text |