On Distortion and Thickness of Knots
dg-ga
2008-02-03 v1 Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.dg-ga/9702001,
title = {On Distortion and Thickness of Knots},
author = {Robert B. Kusner and John M. Sullivan},
journal= {arXiv preprint arXiv:dg-ga/9702001},
year = {2008}
}
Comments
13 pages, LaTeX2e