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Geometric properties and problems of thick knots /
"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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Nova Science Publishers,
©2009.
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| Colección: | Mathematics research developments series.
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| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | "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 theory in fields such as biology and polymer chemistry. In this book, the authors first give a brief review of the basic concepts and terminologies such as the thickness of a knot and the ropelength of a knot. They then review the main results in this field. The topics include results on the global minimum ropelength of knots, various lower and upper ropelength bounds of knots in terms of their crossing numbers, and lower and upper bounds on the total curvatures of thick knots. Some special families of knots or under different settings, such as lattice knots and smooth knots are also considered. While some proofs are omitted or only outlined due to the page limitation of the book, many important ideas, methods, and theorems are explained in depth. At the end of the book, a list of some open problems in this field is given."--Publisher's description |
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| Descripción Física: | 1 online resource (81 pages) : illustrations |
| Bibliografía: | Includes bibliographical references and index. |
| ISBN: | 9781613246290 1613246293 |