On Distortion and Thickness of Knots*

  • Robert B. Kusnert
  • John M. Sullivant
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 103)


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.


Lower Semicontinuous Opposite Point Solid Torus Antipodal Point Regular Neighborhood 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York, Inc. 1998

Authors and Affiliations

  • Robert B. Kusnert
    • 1
  • John M. Sullivant
    • 2
  1. 1.Department of Mathematics, Lederle Graduate Research CenterUniversity of MassachusettsAmherstUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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