Topology and Geometry in Polymer Science
Volume 103 of the series The IMA Volumes in Mathematics and its Applications pp 6776
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
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.
 Title
 On Distortion and Thickness of Knots^{*}
 Book Title
 Topology and Geometry in Polymer Science
 Pages
 pp 6776
 Copyright
 1998
 DOI
 10.1007/9781461217121_7
 Print ISBN
 9780387985800
 Online ISBN
 9781461217121
 Series Title
 The IMA Volumes in Mathematics and its Applications
 Series Volume
 103
 Series ISSN
 09406573
 Publisher
 Springer New York
 Copyright Holder
 SpringerVerlag New York, Inc.
 Additional Links
 Topics
 eBook Packages
 Editors

 Stuart G. Whittington ^{(2)}
 Witt De Sumners ^{(3)}
 Timothy Lodge ^{(4)}
 Editor Affiliations

 2. Department of Chemistry, University of Toronto
 3. Department of Mathematics, Florida State University
 4. Department of Chemistry, University of Minnesota
 Authors

 Robert B. Kusnert ^{(5)}
 John M. Sullivant ^{(6)}
 Author Affiliations

 5. Department of Mathematics, Lederle Graduate Research Center, University of Massachusetts, Amherst, MA, USA
 6. Department of Mathematics, University of Illinois, Urbana, IL, USA
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