On Distortion and Thickness of Knots

Details On Distortion and Thickness of Knots On Distortion and Thickness of Knots

1997-02-04

arxiv.org/abs/dg-ga/9702001v1

in "Topology and Geometry in Polymer Science" (IMA 103), Springer, 1998, pp 67-78

Mathematics

Differential Geometry

13 pages, LaTeX2e

Scientific paper

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.

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