Knot adjacency and satellites
| dc.creator | Kalfagianni, Efstratia | |
| dc.creator | Lin, Xiao-Song | |
| dc.date | 2003-08-18 | |
| dc.date.accessioned | 2026-07-07T05:00:28Z | |
| dc.date.available | 2026-07-07T05:00:28Z | |
| dc.description | A knot K is called n-adjacent to the unknot, if K admits a projection containing n generalized crossings such that changing any m (no larger than n) of them yields a projection of the unknot. We show that a non-trivial satellite knot K is n-adjacent to the unknot, for some n>0, if and only if it is n-adjacent to the unknot in any companion solid torus. In particular, every model knot of K is n-adjacent to the unknot. Along the way of proving these results, we also show that 2-bridge knots of the form K_{p/q}, where p/q=[2q_1,2q_2] for some integers q_1,q_2, are precisely those knots that have genus one and are 2-adjacent to the unknot. | |
| dc.description | 13 pages, 3 figures. to appear in Topology and Its Applications | |
| dc.identifier | https://arxiv.org/abs/math/0308168 | |
| dc.identifier | http://arxiv.org/abs/math/0308168 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68337 | |
| dc.subject | Geometric Topology | |
| dc.title | Knot adjacency and satellites | |
| dc.type | text |