Knot Theory And Its Applications

Author : Kunio Murasugi
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 41,6 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 : 54,8 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 : Louis H. Kauffman
Publisher : World Scientific
Page : 577 pages
File Size : 55,6 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.

Author : W.B.Raymond Lickorish
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206910

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An Introduction to Knot Theory by W.B.Raymond Lickorish Pdf

A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant results are achieved and each chapter ends with exercises and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area.

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 53,7 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 : Kunio Murasugi,Józef Przytycki
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 40,5 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 : American Mathematical Society. Short Course
Publisher : American Mathematical Soc.
Page : 203 pages
File Size : 46,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821844663

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Applications of Knot Theory by American Mathematical Society. Short Course Pdf

Louis Kauffman discusses applications of knot theory to physics, Nadrian Seeman discusses how topology is used in DNA nanotechnology, and Jonathan Simon discusses the statistical and energetic properties of knots and their relation to molecular biology."--BOOK JACKET.

Author : Jessica S. Purcell
Publisher : American Mathematical Soc.
Page : 369 pages
File Size : 48,6 Mb
Release : 2020-10-06
Category : Education
ISBN : 9781470454999

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Hyperbolic Knot Theory by Jessica S. Purcell Pdf

This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of Mostow and Prasad with Gordon and Luecke, it was known that a hyperbolic structure on a knot complement in the 3-sphere gives a complete knot invariant. However, it remains a difficult problem to relate the hyperbolic geometry of a knot to other invariants arising from knot theory. In particular, it is difficult to determine hyperbolic geometric information from a knot diagram, which is classically used to describe a knot. This textbook provides background on these problems, and tools to determine hyperbolic information on knots. It also includes results and state-of-the art techniques on hyperbolic geometry and knot theory to date. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises. The level is appropriate for graduate students with a basic background in algebraic topology, particularly fundamental groups and covering spaces. Some experience with some differential topology and Riemannian geometry will also be helpful.

Author : Akio Kawauchi
Publisher : Birkhäuser
Page : 431 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892278

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A Survey of Knot Theory by Akio Kawauchi Pdf

Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.

Author : Heather A. Dye
Publisher : CRC Press
Page : 256 pages
File Size : 42,7 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781315360096

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An Invitation to Knot Theory by Heather A. Dye Pdf

The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to research knot theory and read journal articles on their own. Each chapter includes numerous examples, problems, projects, and suggested readings from research papers. The proofs are written as simply as possible using combinatorial approaches, equivalence classes, and linear algebra. The text begins with an introduction to virtual knots and counted invariants. It then covers the normalized f-polynomial (Jones polynomial) and other skein invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation.

Author : Kunio Murasugi
Publisher : Unknown
Page : 341 pages
File Size : 50,5 Mb
Release : 2008
Category : Electronic
ISBN : OCLC:1151767223

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Knot Theory & Its Applications by Kunio Murasugi Pdf

Author : Louis H Kauffman
Publisher : World Scientific
Page : 492 pages
File Size : 41,5 Mb
Release : 1995-03-06
Category : Electronic
ISBN : 9789814501439

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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. Contents:Knot Logic (L H Kauffman)On Vortex AtomsOn Vortex MotionVortex Statics (W Thomson)Connection between Spin, Statistics, and Kinks (D Finkelstein & J Rubinstein)Flux Quantization and Particle Physics (H Jehle)Knot Wormholes in Geometrodynamics? (E W Mielke)Helicity and the Calugareanu Invariant (H K Moffatt & R L Ricca)Witten's Invariant of 3-Dimensional Manifolds: Loop Expansion and Surgery Calculus (L Rozansky)2+1 Dimensional Quantum Gravity as a Gaussian Fermionic System and the 3D-Ising Model (M Martellini & M Rasetti)Vassiliev Knot Invariants and the Structure of RNA Folding (L H Kauffman & Y B Magarshak)The Entanglement Structures of Polymers (A MacArthur)Synthesis and Cutting “In Half” of a Molecular Mobius Strip — Applications of Low Dimensional Topology in Chemistry (D W Walba et al.)Turning a Penrose Triangle Inside Out (T M Cowan) Readership: Mathematicians and mathematical physicists. keywords:Topological Gravity;Quantum Geometrodynanics;Knot Wormholes

Author : R. H. Crowell,R. H. Fox
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461299356

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Introduction to Knot Theory by R. H. Crowell,R. H. Fox Pdf

Knot theory is a kind of geometry, and one whose appeal is very direct because the objects studied are perceivable and tangible in everyday physical space. It is a meeting ground of such diverse branches of mathematics as group theory, matrix theory, number theory, algebraic geometry, and differential geometry, to name some of the more prominent ones. It had its origins in the mathematical theory of electricity and in primitive atomic physics, and there are hints today of new applications in certain branches of chemistryJ The outlines of the modern topological theory were worked out by Dehn, Alexander, Reidemeister, and Seifert almost thirty years ago. As a subfield of topology, knot theory forms the core of a wide range of problems dealing with the position of one manifold imbedded within another. This book, which is an elaboration of a series of lectures given by Fox at Haverford College while a Philips Visitor there in the spring of 1956, is an attempt to make the subject accessible to everyone. Primarily it is a text book for a course at the junior-senior level, but we believe that it can be used with profit also by graduate students. Because the algebra required is not the familiar commutative algebra, a disproportionate amount of the book is given over to necessary algebraic preliminaries.

Author : William Menasco,Morwen Thistlethwaite
Publisher : Elsevier
Page : 502 pages
File Size : 47,7 Mb
Release : 2005-08-02
Category : Mathematics
ISBN : 0080459544

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Handbook of Knot Theory by William Menasco,Morwen Thistlethwaite Pdf

This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry. * Survey of mathematical knot theory * Articles by leading world authorities * Clear exposition, not over-technical * Accessible to readers with undergraduate background in mathematics

Author : Krishnendu Gongopadhyay,Rama Mishra
Publisher : American Mathematical Soc.
Page : 357 pages
File Size : 54,8 Mb
Release : 2016-09-21
Category : Knot theory
ISBN : 9781470422578

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Knot Theory and Its Applications by Krishnendu Gongopadhyay,Rama Mishra Pdf

This volume contains the proceedings of the ICTS program Knot Theory and Its Applications (KTH-2013), held from December 10–20, 2013, at IISER Mohali, India. The meeting focused on the broad area of knot theory and its interaction with other disciplines of theoretical science. The program was divided into two parts. The first part was a week-long advanced school which consisted of minicourses. The second part was a discussion meeting that was meant to connect the school to the modern research areas. This volume consists of lecture notes on the topics of the advanced school, as well as surveys and research papers on current topics that connect the lecture notes with cutting-edge research in the broad area of knot theory.