Geometric properties and problems of thick knots / Yuanan Diao and Claus Ernst.
"In geometric knot theory, a central issue is to study the various geometric properties of knots when the knots have certain thickness. This setting makes a knot more like one that is tied with a uniform physical rope. These problems are mostly motivated by the recent applications of knot theor...
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| Format: | eBook |
| Language: | English |
| Published: |
New York :
Nova Science Publishers,
©2009.
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| Series: | Mathematics research developments series.
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Table of Contents:
- Introduction
- Some basic facts of knot theory
- Thicknesses of knots
- Ropelengths of knots
- Smooth knots vs knots on the cubic lattice
- Global lower bound on ropelength of knots
- General lower bounds on ropelength of knots
- General upper bounds on ropelength of knots
- Ropelength upper bounds for special classes of knots
- The spectrum of powers realizable by thick knots
- Total curvature of thick knots
- The linking number of a thick link with two or more components
- Some open questions.