Download or read book An Introduction to Knot Theory written by W.B.Raymond Lickorish and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Knot Theory written by R. H. Crowell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Interactive Introduction to Knot Theory written by Inga Johnson and published by Courier Dover Publications. This book was released on 2017-01-04 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well-written and engaging, this hands-on approach features many exercises to be completed by readers. Topics include knot definition and equivalence, combinatorial and algebraic invariants, unknotting operations, and virtual knots. 2016 edition.
Download or read book The Knot Book written by Colin Conrad Adams and published by American Mathematical Soc.. This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Survey of Knot Theory written by Akio Kawauchi and published by Birkhäuser. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Formal Knot Theory written by Louis H. Kauffman and published by Courier Corporation. This book was released on 2006-01-01 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author, Louis H. Kauffman, is a professor in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago. Kauffman draws upon his work as a topologist to illustrate the relationships between knot theory and statistical mechanics, quantum theory, and algebra, as well as the role of knot theory in combinatorics. Featured topics include state, trails, and the clock theorem; state polynomials and the duality conjecture; knots and links; axiomatic link calculations; spanning surfaces; the genus of alternative links; and ribbon knots and the Arf invariant. Key concepts are related in easy-to-remember terms, and numerous helpful diagrams appear throughout the text. The author has provided a new supplement, entitled "Remarks on Formal Knot Theory," as well as his article, "New Invariants in the Theory of Knots," first published in The American Mathematical Monthly, March 1988.
Download or read book Why Knot written by Colin Adams and published by Springer Science & Business Media. This book was released on 2004-03-29 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Colin Adams, well-known for his advanced research in topology and knot theory, is the author of this exciting new book that brings his findings and his passion for the subject to a more general audience. This beautifully illustrated comic book is appropriate for many mathematics courses at the undergraduate level such as liberal arts math, and topology. Additionally, the book could easily challenge high school students in math clubs or honors math courses and is perfect for the lay math enthusiast. Each copy of Why Knot? is packaged with a plastic manipulative called the Tangle R. Adams uses the Tangle because "you can open it up, tie it in a knot and then close it up again." The Tangle is the ultimate tool for knot theory because knots are defined in mathematics as being closed on a loop. Readers use the Tangle to complete the experiments throughout the brief volume. Adams also presents a illustrative and engaging history of knot theory from its early role in chemistry to modern applications such as DNA research, dynamical systems, and fluid mechanics. Real math, unreal fun!
Download or read book Hyperbolic Knot Theory written by Jessica S. Purcell and published by American Mathematical Soc.. This book was released on 2020-10-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Knot Theory and Its Applications written by Kunio Murasugi and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Knot Theory written by Charles Livingston and published by American Mathematical Soc.. This book was released on 1993-12-31 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot Theory, a lively exposition of the mathematics of knotting, will appeal to a diverse audience from the undergraduate seeking experience outside the traditional range of studies to mathematicians wanting a leisurely introduction to the subject. Graduate students beginning a program of advanced study will find a worthwhile overview, and the reader will need no training beyond linear algebra to understand the mathematics presented. The interplay between topology and algebra, known as algebraic topology, arises early in the book when tools from linear algebra and from basic group theory are introduced to study the properties of knots. Livingston guides readers through a general survey of the topic showing how to use the techniques of linear algebra to address some sophisticated problems, including one of mathematics's most beautiful topics—symmetry. The book closes with a discussion of high-dimensional knot theory and a presentation of some of the recent advances in the subject—the Conway, Jones, and Kauffman polynomials. A supplementary section presents the fundamental group which is a centerpiece of algebraic topology.
Download or read book Teaching and Learning of Knot Theory in School Mathematics written by Akio Kawauchi and published by Springer Science & Business Media. This book was released on 2012-06-27 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of a joint venture between Professor Akio Kawauchi, Osaka City University, well-known for his research in knot theory, and the Osaka study group of mathematics education, founded by Professor Hirokazu Okamori and now chaired by his successor Professor Tomoko Yanagimoto, Osaka Kyoiku University. The seven chapters address the teaching and learning of knot theory from several perspectives. Readers will find an extremely clear and concise introduction to the fundamentals of knot theory, an overview of curricular developments in Japan, and in particular a series of teaching experiments at all levels which not only demonstrate the creativity and the professional expertise of the members of the study group, but also give a lively impression of students’ learning processes. In addition the reports show that elementary knot theory is not just a preparation for advanced knot theory but also an excellent means to develop spatial thinking. The book can be highly recommended for several reasons: First of all, and that is the main intention of the book, it serves as a comprehensive text for teaching and learning knot theory. Moreover it provides a model for cooperation between mathematicians and mathematics educators based on substantial mathematics. And finally it is a thorough introduction to the Japanese art of lesson studies–again in the context of substantial mathematics.
Download or read book Introductory Lectures on Knot Theory written by Louis H. Kauffman and published by World Scientific. This book was released on 2012 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Knots and Primes written by Masanori Morishita and published by Springer Nature. This book was released on with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopedia of Knot Theory written by Colin Adams and published by CRC Press. This book was released on 2022-12-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This books provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications edited and contributed to by top researchers in the field of knot theory. The articles in this book are accessible to both undergrads and researchers.
Download or read book A Gentle Introduction To Knots Links And Braids written by Ruben Aldrovandi and published by World Scientific. This book was released on 2021-10-14 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.
Download or read book Quandles written by Mohamed Elhamdadi and published by American Mathematical Soc.. This book was released on 2015-08-27 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: From prehistory to the present, knots have been used for purposes both artistic and practical. The modern science of Knot Theory has ramifications for biochemistry and mathematical physics and is a rich source of research projects for undergraduate and graduate students and professionals alike. Quandles are essentially knots translated into algebra. This book provides an accessible introduction to quandle theory for readers with a background in linear algebra. Important concepts from topology and abstract algebra motivated by quandle theory are introduced along the way. With elementary self-contained treatments of topics such as group theory, cohomology, knotted surfaces and more, this book is perfect for a transition course, an upper-division mathematics elective, preparation for research in knot theory, and any reader interested in knots.
Download or read book Knots And Physics Second Edition written by Louis H Kauffman and published by World Scientific. This book was released on 1994-01-15 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included.This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems.
