Title
Thickness of knots
Department/School
Mathematics
Date
2-24-1999
Document Type
Article
Keywords
classical knot theory, knots, ropelength
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.
Volume
91
Issue
3
Published in
Topology and its Applications
COinS
Citation/Other Information
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