Unknotting numbers of diagrams of a given nontrivial knot are unbounded
| dc.creator | Taniyama, Kouki | |
| dc.date | 2008-05-20 | |
| dc.date | 2008-06-22 | |
| dc.date.accessioned | 2026-07-07T09:45:42Z | |
| dc.date.available | 2026-07-07T09:45:42Z | |
| dc.description | We show that for any nontrivial knot $K$ and any natural number $n$ there is a diagram $D$ of $K$ such that the unknotting number of $D$ is greater than or equal to $n$. It is well known that twice the unknotting number of $K$ is less than or equal to the crossing number of $K$ minus one. We show that the equality holds only when $K$ is a $(2,p)$-torus knot. | |
| dc.description | 13 pages, 14 figures. Theorem 1.4 and Theorem 1.5 added | |
| dc.identifier | https://arxiv.org/abs/0805.3174 | |
| dc.identifier | http://arxiv.org/abs/0805.3174 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163286 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 | |
| dc.title | Unknotting numbers of diagrams of a given nontrivial knot are unbounded | |
| dc.type | text |