The number of Reidemeister Moves Needed for Unknotting
| dc.creator | Hass, Joel | |
| dc.creator | Lagarias, Jeffrey C. | |
| dc.date | 1998-07-02 | |
| dc.date.accessioned | 2026-07-07T05:25:15Z | |
| dc.date.available | 2026-07-07T05:25:15Z | |
| dc.description | There is a positive constant $c_1$ such that for any diagram $D$ representing the unknot, there is a sequence of at most $2^{c_1 n}$ Reidemeister moves that will convert it to a trivial knot diagram, $n$ is the number of crossings in $D$. A similar result holds for elementary moves on a polygonal knot $K$ embedded in the 1-skeleton of the interior of a compact, orientable, triangulated $PL$ 3-manifold $M$. There is a positive constant $c_2$ such that for each $t \geq 1$, if $M$ consists of $t$ tetrahedra, and $K$ is unknotted, then there is a sequence of at most $2^{c_2 t}$ elementary moves in $M$ which transforms $K$ to a triangle contained inside one tetrahedron of $M$. We obtain explicit values for $c_1$ and $c_2$. | |
| dc.description | 48 pages, 14 figures | |
| dc.identifier | https://arxiv.org/abs/math/9807012 | |
| dc.identifier | http://arxiv.org/abs/math/9807012 | |
| dc.identifier | J. Amer. Math. Soc. 14 (2001), 399--428. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77114 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25; 68Q25 | |
| dc.title | The number of Reidemeister Moves Needed for Unknotting | |
| dc.type | text |