Thickness of knots
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
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