Thickness of knots

Authors

R. A. Litherland, Louisiana State University
J. Simon, University of Iowa
O. Durumeric, University of Iowa
E. Rawdon, University of Iowa

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