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The Theory Of Quantum Torus Knots
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Book Synopsis The Knot Book by : Colin Conrad Adams
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 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.""
Book Synopsis The Theory of Quantum Torus Knots by :
Download or read book The Theory of Quantum Torus Knots written by and published by . This book was released on 2020-05-06 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Knot Theory and Its Applications by : Kunio Murasugi
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.
Author :W.B.Raymond Lickorish Publisher :Springer Science & Business Media ISBN 13 :146120691X Total Pages :213 pages Book Rating :4.4/5 (612 download)
Book Synopsis An Introduction to Knot Theory by : W.B.Raymond Lickorish
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.
Book Synopsis Introduction to Topological Quantum Computation by : Jiannis K. Pachos
Download or read book Introduction to Topological Quantum Computation written by Jiannis K. Pachos and published by Cambridge University Press. This book was released on 2012-04-12 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. Special emphasis is given to the motivation and physical intuition behind every mathematical concept. Demystifying difficult topics by using accessible language, this book has broad appeal and is ideal for graduate students and researchers from various disciplines who want to get into this new and exciting research field.
Book Synopsis Knots and Feynman Diagrams by : Dirk Kreimer
Download or read book Knots and Feynman Diagrams written by Dirk Kreimer and published by Cambridge University Press. This book was released on 2000-07-20 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explains how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. The author emphasizes how new discoveries in mathematics have inspired conventional calculational methods for perturbative quantum field theory to become more elegant and potentially more powerful methods. The material illustrates what may possibly be the most productive interface between mathematics and physics. As a result, it will be of interest to graduate students and researchers in theoretical and particle physics as well as mathematics.
Book Synopsis Introductory Lectures on Knot Theory by : Louis H. Kauffman
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.
Book Synopsis The Theory of Quantum Torus Knots by : Michael Ungs
Download or read book The Theory of Quantum Torus Knots written by Michael Ungs and published by Lulu.com. This book was released on 2009-11-06 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed mathematical derivation of space curves is presented that links the diverse fields of superfluids, quantum mechanics, and hydrodynamics by a common foundation. The basic mathematical building block is called the theory of quantum torus knots (QTK).
Book Synopsis The Geometry and Physics of Knots by : Michael Francis Atiyah
Download or read book The Geometry and Physics of Knots written by Michael Francis Atiyah and published by Cambridge University Press. This book was released on 1990-08-23 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes deal with an area that lies at the crossroads of mathematics and physics and rest primarily on the pioneering work of Vaughan Jones and Edward Witten, who related polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions.
Book Synopsis Hyperbolic Knot Theory by : Jessica S. Purcell
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 392 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.
Book Synopsis A Survey of Knot Theory by : Akio Kawauchi
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.
Book Synopsis Differential and Symplectic Topology of Knots and Curves by : Serge Tabachnikov
Download or read book Differential and Symplectic Topology of Knots and Curves written by Serge Tabachnikov and published by American Mathematical Soc.. This book was released on 1999 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of papers on two related topics: topology of knots and knot-like objects (such as curves on surfaces) and topology of Legendrian knots and links in 3-dimensional contact manifolds. Featured is the work of international experts in knot theory ("quantum" knot invariants, knot invariants of finite type), in symplectic and contact topology, and in singularity theory. The interplay of diverse methods from these fields makes this volume unique in the study of Legendrian knots and knot-like objects such as wave fronts. A particularly enticing feature of the volume is its international significance. The volume successfully embodies a fine collaborative effort by worldwide experts from Belgium, France, Germany, Israel, Japan, Poland, Russia, Sweden, the UK, and the US.
Book Synopsis Grid Homology for Knots and Links by : Peter S. Ozsváth
Download or read book Grid Homology for Knots and Links written by Peter S. Ozsváth and published by American Mathematical Soc.. This book was released on 2015-12-04 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Quantum and Vassiliev Knot Invariants by : David M. Jackson
Download or read book An Introduction to Quantum and Vassiliev Knot Invariants written by David M. Jackson and published by Springer. This book was released on 2019-05-04 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant.
Book Synopsis Encyclopedia of Knot Theory by : Colin Adams
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
Book Synopsis Knots and Physics by : Louis H. Kauffman
Download or read book Knots and Physics written by Louis H. Kauffman and published by World Scientific. This book was released on 1991 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory explication on the theme of knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of the knot theory, coupled with a quantum statistical frame work create a context that naturally and powerfully includes an extraordinary range of interelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward the 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 with and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics, knots in dynamical systems.
