Title

Thickness of knots

Document Type

Article

Publication Date

1-1-1999

Abstract

Classical knot theory studies one-dimensional filaments; in this paper we model knots as more physically "real", e.g., made of some "rope" with nonzero 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(K) is the supremum of radii of embedded tubular neighborhoods. The "thickness" of K, a new measure of knot complexity, is the ratio of R(K) to arc-length. We relate thickness to curvature, self-distance, distortion, and (for knot types) edge-number. © 1999 Elsevier Science B.V. All rights reserved.

Publication Source (Journal or Book title)

Topology and its Applications

First Page

233

Last Page

244

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