Journal article
Thickness of knots
Topology and its applications, Vol.91(3), pp.233-244
1999
DOI: 10.1016/S0166-8641(97)00210-1
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.
Details
- Title: Subtitle
- Thickness of knots
- Creators
- R.A Litherland - Louisiana State UniversityJ Simon - University of IowaO Durumeric - University of IowaE Rawdon - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Topology and its applications, Vol.91(3), pp.233-244
- DOI
- 10.1016/S0166-8641(97)00210-1
- ISSN
- 0166-8641
- eISSN
- 1879-3207
- Publisher
- Elsevier B.V
- Language
- English
- Date published
- 1999
- Academic Unit
- Mathematics
- Record Identifier
- 9984241039602771
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