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Thickness of knots

✍ Scribed by R.A. Litherland; J. Simon; O. Durumeric; E. Rawdon

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 814 KB
Volume: 91
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(97)00210-1

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✦ Synopsis

Classical knot theory studies one-dimensional filaments; in this paper we model knots as more physically "real". e.g., made of some "rope" with nonLero thickness. A motivating question is: How much length of unit radius rope is needed to tie a nontrivial knot?

For a smooth knot K, the "injectivity radius" R(I<) is the supremum of radii of embedded tubular neighborhoods. The "thickness" of Ii, a new measure of knot complexity, is the ratio of R( IY) to arc-length. We relate thickness to curvature. self-distance. distortion, and (for knot types) edge-number.

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