Total Curvature and Packing of Knots
| dc.creator | Buck, Gregory | |
| dc.creator | Simon, Jonathan | |
| dc.date | 2003-10-22 | |
| dc.date | 2004-01-16 | |
| dc.date.accessioned | 2026-07-07T05:02:11Z | |
| dc.date.available | 2026-07-07T05:02:11Z | |
| dc.description | We establish a new fundamental relationship between total curvature of knots and crossing number. If K is a smooth knot in 3-space, R the cross-section radius of a uniform tube neighborhood of K, L the arclength of K, and k the total curvature of K, then (up to a coefficient independent of K), crossing number of K < (k)(L/R). There are families of knots whose crossing numbers grow faster than either k or L/R separately. For example, the knots whose crossing numbers grow with the (4/3)-power of ropelength must have total curvature growing arbitrarily large as well. | |
| dc.description | 19 pages, no figures. This update of the Oct. 03 version has improved Lemma 1.1 and resulting improved coefficients | |
| dc.identifier | https://arxiv.org/abs/math/0310365 | |
| dc.identifier | http://arxiv.org/abs/math/0310365 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68960 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 57M25 | |
| dc.title | Total Curvature and Packing of Knots | |
| dc.type | text |