Knots And Applications

Author : Louis H. Kauffman
Publisher : World Scientific
Page : 502 pages
File Size : 48,9 Mb
Release : 1995
Category : Science
ISBN : 9810220049

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Knots and Applications by Louis H. Kauffman Pdf

This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Thomson) on the 19th century theory of vortex atoms, reprints of modern papers on knotted flux in physics and in fluid dynamics and knotted wormholes in general relativity. It also includes papers on Witten's approach to knots via quantum field theory and applications of this approach to quantum gravity and the Ising model in three dimensions. Other papers discuss the topology of RNA folding in relation to invariants of graphs and Vassiliev invariants, the entanglement structures of polymers, the synthesis of molecular Mobius strips and knotted molecules. The book begins with an article on the applications of knot theory to the foundations of mathematics and ends with an article on topology and visual perception. This volume will be of immense interest to all workers interested in new possibilities in the uses of knots and knot theory.

Author : Clifford W. Ashley
Publisher : BoD – Books on Demand
Page : 630 pages
File Size : 46,5 Mb
Release : 2023-06-20
Category : Reference
ISBN : 9783963320002

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THE ASHLEY BOOK OF KNOTS by Clifford W. Ashley Pdf

What else needs to be said about knots? Almost 650 pages of incredible knowledge, presented in a truzly unique manner. This is not a book of knots, it is the BOOK OF KNOTS. Was muss noch über Knoten gesagt werden? Fast 650 Seiten unglaubliches Wissen, präsentiert in einer wahrhaft einzigartigen Weise. Dies ist kein Buch über Knoten, es ist das BUCH DER KNOTEN.

Author : Kunio Murasugi
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 47,8 Mb
Release : 2009-12-29
Category : Mathematics
ISBN : 9780817647193

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Knot Theory and Its Applications by Kunio Murasugi Pdf

This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.

Author : Markus Banagl,Denis Vogel
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 41,6 Mb
Release : 2010-11-25
Category : Mathematics
ISBN : 9783642156373

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The Mathematics of Knots by Markus Banagl,Denis Vogel Pdf

The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 40,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821836781

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The Knot Book by Colin Conrad Adams Pdf

Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

Author : Peter R. Cromwell
Publisher : Cambridge University Press
Page : 356 pages
File Size : 44,6 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 0521548314

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Knots and Links by Peter R. Cromwell Pdf

A richly illustrated 2004 textbook on knot theory; minimal prerequisites but modern in style and content.

Author : Randy Penn
Publisher : Simon and Schuster
Page : 288 pages
File Size : 53,5 Mb
Release : 2004-03-05
Category : Sports & Recreation
ISBN : 9781440522772

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The Everything Knots Book by Randy Penn Pdf

Simple instructions on how to tie over 100 useful and decorative knots A well-tied knot is at once a practical tool and a work of art. With names like "hangman's noose" and "wagoneer's hitch," knots have a rich history of usefulness and an aesthetic appeal all their own. From the boat to the backyard, The Everything Knots Book provides simple instructions on how to tie knots for any situation. Written by Randy Penn, a member of the International Guild of Knot Tyers, this handy guide walks readers through the basics and offers myriad suggestions for creative uses of these knots. Mr. Penn shows readers how to: Choose the right rope and knot for the job Tie knots safely and securely Create decorative knots for clothing and accessories Practice knot-tying through games and exercises Packed with easy-to-follow instructions and clear illustrations, The Everything Knots Book makes learning this useful skill fun and easy.

Author : Peter S. Ozsváth,András I. Stipsicz,Zoltán Szabó
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 40,6 Mb
Release : 2015-12-04
Category : Homology theory
ISBN : 9781470417376

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Grid Homology for Knots and Links by Peter S. Ozsváth,András I. Stipsicz,Zoltán Szabó Pdf

Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.

Author : Colin C. Adams,Cameron McA. Gordon,Vaughan F.R. Jones,Louis H. Kauffman,Sofia Lambropoulou,Kenneth C. Millett,Jozef H. Przytycki,Renzo Ricca,Radmila Sazdanovic
Publisher : Springer
Page : 476 pages
File Size : 52,7 Mb
Release : 2019-06-26
Category : Mathematics
ISBN : 9783030160319

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Knots, Low-Dimensional Topology and Applications by Colin C. Adams,Cameron McA. Gordon,Vaughan F.R. Jones,Louis H. Kauffman,Sofia Lambropoulou,Kenneth C. Millett,Jozef H. Przytycki,Renzo Ricca,Radmila Sazdanovic Pdf

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.

Author : Kunio Murasugi,Józef Przytycki
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 42,7 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825709

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An Index of a Graph with Applications to Knot Theory by Kunio Murasugi,Józef Przytycki Pdf

This book presents a remarkable application of graph theory to knot theory. In knot theory, there are a number of easily defined geometric invariants that are extremely difficult to compute; the braid index of a knot or link is one example. The authors evaluate the braid index for many knots and links using the generalized Jones polynomial and the index of a graph, a new invariant introduced here. This invariant, which is determined algorithmically, is likely to be of particular interest to computer scientists.

Author : Jeff Jepson
Publisher : Unknown
Page : 184 pages
File Size : 55,8 Mb
Release : 2013
Category : Knots and splices
ISBN : 0972667911

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Knots at Work by Jeff Jepson Pdf

Author : Derek Hansen
Publisher : CreateSpace
Page : 129 pages
File Size : 47,5 Mb
Release : 2011-10-27
Category : Sports & Recreation
ISBN : 1466263687

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The Ultimate Hang by Derek Hansen Pdf

Hammock camping--one of the most comfortable ways to enjoy a long-distance thru-hike, a weekend backpacking trip, or just an overnight in the woods. With more than 200 illustrations to guide you, this book helps you get off the ground to discover the freedom, comfort, and convenience of hammock camping. Learn how to set up and use a hammock to stay dry, warm, and bug free in a Leave No Trace-friendly way. This book covers hammock camping basics such as how to get a perfect hang and how to stay dry, warm, and bug free. Plus, it illustrates techniques and tips to get the most out of a hammock shelter, whether you have purchased an all-in-one kit or you've assembled your own customized system.

Author : J C Turner,P van de Griend
Publisher : World Scientific
Page : 464 pages
File Size : 40,6 Mb
Release : 1996-05-30
Category : Mathematics
ISBN : 9789814499644

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History and Science of Knots by J C Turner,P van de Griend Pdf

This book brings together twenty essays on diverse topics in the history and science of knots. It is divided into five parts, which deal respectively with knots in prehistory and antiquity, non-European traditions, working knots, the developing science of knots, and decorative and other aspects of knots. Its authors include archaeologists who write on knots found in digs of ancient sites (one describes the knots used by the recently discovered Ice Man); practical knotters who have studied the history and uses of knots at sea, for fishing and for various life support activities; a historian of lace; a computer scientist writing on computer classification of doilies; and mathematicians who describe the history of knot theories from the eighteenth century to the present day. In view of the explosion of mathematical theories of knots in the past decade, with consequential new and important scientific applications, this book is timely in setting down a brief, fragmentary history of mankind's oldest and most useful technical and decorative device — the knot. Contents:Prehistory and Antiquity:Pleistocene KnottingWhy Knot? — Some Speculations on the First KnotsOn Knots and Swamps — Knots in European PrehistoryAncient Egyptian Rope and KnotsNon-European Traditions:The Peruvian QuipuThe Art of Chinese Knots Works: A Short HistoryInuit KnotsWorking Knots:Knots at SeaA History of Life Support KnotsTowards a Science of Knots?:Studies on the Behaviour of KnotsA History of Topological Knot Theory of KnotsTramblesCrochet Work — History and Computer ApplicationsDecorative Knots and Other Aspects:The History of MacraméA History of LaceHeraldic KnotsOn the True Love Knotand other papers Readership: Mathematicians, archeologists, social historians and general readers. keywords:Antiquit;Braiding;Climbing;Heraldry;History;Knots;Lace;Mariners;Prehistory;Quipus;Science;Theory;Topology;Knotting, Pleistocene;Egyptian;Inuit;Chinese;Mountaineering, Topological Knot Theory;Knot Theories;Quipo Knot Mathematics;Knot Strength Efficiency;Heraldic;True Love;Crochet;Computer Aided Design;Trambles “… it is a veritable compendium of information about every aspects of knots, from their links with quantum theory to attempts to measure their strength when tying climbing ropes together … the huge scope of this book makes it one I have turned to many times, for many different purposes.” New Scientists “I enjoyed browsing through all the chapters. They contain material that a mathematician would not normally come across in his work.” The Mathematical Intelligencer

Author : Andrzej Stasiak,Vsevolod Katritch,Louis H. Kauffman
Publisher : World Scientific
Page : 426 pages
File Size : 48,6 Mb
Release : 1998
Category : Mathematics
ISBN : 9789810235307

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Ideal Knots by Andrzej Stasiak,Vsevolod Katritch,Louis H. Kauffman Pdf

In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of knotted arrangements of bistable chemical systems, the trajectories of knotted solitons, and the shapes of knots which can be tied using the shortest piece of elastic rope with a constant diameter.

Author : Louis H. Kauffman
Publisher : World Scientific
Page : 577 pages
File Size : 47,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814313001

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Introductory Lectures on Knot Theory by Louis H. Kauffman Pdf

More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.