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 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 Handbook of Knot Theory written by William Menasco and published by Elsevier. This book was released on 2005-08-02 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
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 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 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 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-written and engaging volume, intended for undergraduates, introduces knot theory, an area of growing interest in contemporary mathematics. The hands-on approach features many exercises to be completed by readers. Prerequisites are only a basic familiarity with linear algebra and a willingness to explore the subject in a hands-on manner. The opening chapter offers activities that explore the world of knots and links — including games with knots — and invites the reader to generate their own questions in knot theory. Subsequent chapters guide the reader to discover the formal definition of a knot, families of knots and links, and various knot notations. Additional topics include combinatorial knot invariants, knot polynomials, unknotting operations, and virtual knots.
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 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 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 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 Knots and Primes written by Masanori Morishita and published by Springer Science & Business Media. This book was released on 2011-11-27 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory. Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry.
Download or read book An Invitation to Knot Theory written by Heather A. Dye and published by CRC Press. This book was released on 2018-09-03 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Knots and Links written by Dale Rolfsen and published by American Mathematical Soc.. This book was released on 2003 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book.""
Download or read book Knot Theory written by Vassily Olegovich Manturov and published by CRC Press. This book was released on 2018-04-17 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition is notable not only for its expert presentation of knot theory’s state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.
Download or read book Encyclopedia of Knot Theory written by Colin Adams and published by CRC Press. This book was released on 2021-02-10 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory
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 578 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.
