  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.

Differential Geometry;Differential Geometry