On Distortion and Thickness of Knots

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

What length of rope (of given diameter) is required to tie a particular knot? To answer this question, we define some new notions of thickness for a space curve, one based on Gromov's distortion, and another generalizing the thickness of Litherland, Simon et al. We prove a basic inequality between these thickness measures, and show that the distortion thickness is upper semi-continuous in the C^0 topology, suggesting that shortest curves of thickness 1 should exist in each knot class.
13 pages, LaTeX2e

Keywords

Differential Geometry

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/152202

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/dg-ga/9702001
 http://arxiv.org/abs/dg-ga/9702001
 in "Topology and Geometry in Polymer Science" (IMA 103), Springer, 1998, pp 67-78

Collections

arXiv