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
Recommended Citation
Litherland, R., Simon, J., Durumeric, O., & Rawdon, E. (1999). Thickness of knots. Topology and its Applications, 91 (3), 233-244. https://doi.org/10.1016/s0166-8641(97)00210-1