The Distortion of a Knotted Curve
| dc.creator | Denne, Elizabeth | |
| dc.creator | Sullivan, John M | |
| dc.date | 2004-09-22 | |
| dc.date | 2007-12-29 | |
| dc.date.accessioned | 2026-07-07T08:51:28Z | |
| dc.date.available | 2026-07-07T08:51:28Z | |
| dc.description | The distortion of a curve measures the maximum arc/chord length ratio. Gromov showed any closed curve has distortion at least pi/2 and asked about the distortion of knots. Here, we prove that any nontrivial tame knot has distortion at least 5pi/3; examples show that distortion under 7.16 suffices to build a trefoil knot. Our argument uses the existence of a shortest essential secant and a characterization of borderline-essential arcs. | |
| dc.description | 5 pages, 7 figures; substantial improvements: bound is now 5pi/3 and applies to all tame knots | |
| dc.identifier | https://arxiv.org/abs/math/0409438 | |
| dc.identifier | http://arxiv.org/abs/math/0409438 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144946 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 57M25 (Primary); 49Q10, 53A04, 53C42 (Secondary) | |
| dc.title | The Distortion of a Knotted Curve | |
| dc.type | text |