On Distortion and Thickness of Knots*

  • Robert B. Kusnert
  • John M. Sullivant

Abstract

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.

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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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