Topology and Geometry in Polymer Science

Volume 103 of the series The IMA Volumes in Mathematics and its Applications pp 67-76

On Distortion and Thickness of Knots*

  • Robert B. KusnertAffiliated withDepartment of Mathematics, Lederle Graduate Research Center, University of Massachusetts
  • , John M. SullivantAffiliated withDepartment of Mathematics, University of Illinois

* Final gross prices may vary according to local VAT.

Get Access


What length of rope (of given diameter) is required to tie a particular knot ? Or, to turn the problem around, given an embedded curve, how thick a regular neighborhood of the curve also is embedded ? Intuitively, the diameter of the possible rope is bounded by the distance between strands at the closest crossing in the knot. But of course the distance between two points along a curve goes to zero as the points approach each other, so to make the notion precise, we need to exclude some neighborhood of the diagonal.