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Knots and Knot Theory books

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Introduction to Knot Theory
By R.H.Crowell and R.H.Fox

• Publisher: Blaisdell
• Number Of Pages:
• Publication Date: 1963
• ISBN-10 / ASIN: B000LZKFGI
• ISBN-13 / EAN:
• Binding: Hardcover

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Knot Theory
By Vassily Manturov

• Publisher: CRC
• Number Of Pages: 416
• Publication Date: 2004-02-24
• ISBN-10 / ASIN: 0415310016
• ISBN-13 / EAN: 9780415310017
• Binding: Hardcover

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Product Description:

Since discovery of the Jones polynomial, knot theory has enjoyed a virtual explosion of important results and now plays a significant role in modern mathematics. In a unique presentation with contents not found in any other monograph, Knot Theory describes, with full proofs, the main concepts and the latest investigations in the field. The book is divided into six thematic sections. The first part discusses "pre-Vassiliev" knot theory, from knot arithmetics through the Jones polynomial and the famous Kauffman-Murasugi theorem. The second part explores braid theory, including braids in different spaces and simple word recognition algorithms. A section devoted to the Vassiliev knot invariants follows, wherein the author proves that Vassiliev invariants are stronger than all polynomial invariants and introduces Bar-Natan's theory on Lie algebra respresentations and knots. The fourth part describes a new way, proposed by the author, to encode knots by d-diagrams. This method allows the encoding of topological objects by words in a finite alphabet. Part Five delves into virtual knot theory and virtualizations of knot and link invariants. This section includes the author's own important results regarding new invariants of virtual knots. The book concludes with an introduction to knots in 3-manifolds and Legendrian knots and links, including Chekanov's differential graded algebra (DGA) construction. Knot Theory 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 professional reference and will serve equally well as a text for a course on knot theory.​

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Handbook of Knot Theory
By William Menasco

• Publisher: Elsevier Science
• Number Of Pages: 502
• Publication Date: 2005-07-09
• Sales Rank: 1165317
• ISBN / ASIN: 044451452X
• EAN: 9780444514523
• Binding: Hardcover
• Manufacturer: Elsevier Science
• Studio: Elsevier Science
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Book Description:

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​

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Knots: Mathematics with a Twist
By Alexei Sossinsky

• Publisher: Harvard University Press
• Number Of Pages: 160
• Publication Date: 2002-12-31
• ISBN-10 / ASIN: 0674009444
• ISBN-13 / EAN: 9780674009448
• Binding: Hardcover

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Product Description:

Ornaments and icons, symbols of complexity or evil, aesthetically appealing and endlessly useful in everyday ways, knots are also the object of mathematical theory, used to unravel ideas about the topological nature of space. In recent years knot theory has been brought to bear on the study of equations describing weather systems, mathematical models used in physics, and even, with the realization that DNA sometimes is knotted, molecular biology.
This book, written by a mathematician known for his own work on knot theory, is a clear, concise, and engaging introduction to this complicated subject. A guide to the basic ideas and applications of knot theory, Knots takes us from Lord Kelvin's early--and mistaken--idea of using the knot to model the atom, almost a century and a half ago, to the central problem confronting knot theorists today: distinguishing among various knots, classifying them, and finding a straightforward and general way of determining whether two knots--treated as mathematical objects--are equal.
Communicating the excitement of recent ferment in the field, as well as the joys and frustrations of his own work, Alexei Sossinsky reveals how analogy, speculation, coincidence, mistakes, hard work, aesthetics, and intuition figure far more than plain logic or magical inspiration in the process of discovery. His spirited, timely, and lavishly illustrated work shows us the pleasure of mathematics for its own sake as well as the surprising usefulness of its connections to real-world problems in the sciences. It will instruct and delight the expert, the amateur, and the curious alike. ​

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Physical and Numerical Models in Knot Theory: Including Applications to The Life Sciences
By et al Jorge A. Calvo (Editor)

• Publisher: World Scientific Publishing Company
• Number Of Pages: 628
• Publication Date: 2005-09
• Sales Rank: 1905952
• ISBN / ASIN: 9812561870
• EAN: 9789812561879
• Binding: Hardcover
• Manufacturer: World Scientific Publishing Company
• Studio: World Scientific Publishing Company
• Average Rating:
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Product Description:

The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year. This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory.​

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High-dimensional Knot Theory: Algebraic Surgery in Codimension 2 (Springer Monographs in Mathematics)
By Andrew Ranicki

• Publisher: Springer
• Number Of Pages: 646
• Publication Date: 1998-09-18
• ISBN-10 / ASIN: 3540633898
• ISBN-13 / EAN: 9783540633891
• Binding: Hardcover

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Product Description:

High-dimensional knot theory is the study of the embeddings of n-dimensional manifolds in (n+2)-dimensional manifolds, generalizing the traditional study of knots in the case n=1. The main theme is the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory. Many results in the research literature are thus brought into a single framework, and new results are obtained. The treatment is particularly effective in dealing with open books, which are manifolds with codimension 2 submanifolds such that the complement fibres over a circle. The book concludes with an appendix by E. Winkelnkemper on the history of open books.​

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Knots and Surfaces
By N. D. Gilbert, T. Porter, N.d. Gilbert

• Publisher: Oxford University Press, USA
• Number Of Pages: 268
• Publication Date: 1994-01-15
• ISBN-10 / ASIN: 0198533977
• ISBN-13 / EAN: 9780198533979
• Binding: Hardcover

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Product Description:

This highly readable text details the interaction between the mathematical theory of knots and the theories of surfaces and group presentations. It expertly introduces several topics critical to the development of pure mathematics while providing an account of math "in action" in an unusual context. Beginning with a simple diagrammatic approach to the study of knots that reflects the artistic and geometric appeal of interlaced forms, Knots and Surfaces takes the reader through recent research advances. Topics include topological spaces, surfaces, the fundamental group, graphs, free groups, and group presentations. The authors skillfully combine these topics to form a coherent and highly developed theory to explore and explain the accessible and intuitive problems of knots and surfaces to students and researchers in mathematics.​

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Knots (De Gruyter Studies in Mathematics, 5)
By Gerhard Burde, Heiner Zieschang

• Publisher: Walter de Gruyter
• Number Of Pages: 559
• Publication Date: 2002-12-01
• ISBN-10 / ASIN: 3110170051
• ISBN-13 / EAN: 9783110170054
• Binding: Hardcover

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Book Description:

This book is an introduction to classical knot theory. Topics covered include: different constructions of knots, knot diagrams, knot groups, fibred knots, characterisation of torus knots, prime decomposition of knots, cyclic coverings and Alexander polynomials and modules together with the free differential calculus, braids, branched coverings and knots, Montesinos links, representations of knot groups, surgery of 3-manifolds and knots.
Knot theory has expanded enormously since the first edition of this book published in 1985. A special feature of this second completely revised and extended edition is the introduction to two new constructions of knot invariants, namely the Jones and homfly polynomials and the Vassiliev invariants.
The book contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory.
Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known. The text is accessible to advanced undergraduate and graduate students in mathematics.​

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Knots and Links (AMS Chelsea Publishing)
By Dale Rolfsen

• Publisher: American Mathematical Society
• Number Of Pages: 439
• Publication Date: 2003-12
• ISBN-10 / ASIN: 0821834363
• ISBN-13 / EAN: 9780821834367
• Binding: Hardcover

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Product Description:

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.​

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Knots and Quantum Gravity (Oxford Lecture Series in Mathematics and Its Applications, No 1)
By John C. Baez

• Publisher: Oxford University Press, USA
• Number Of Pages: 248
• Publication Date: 1994-12-01
• ISBN-10 / ASIN: 0198534906
• ISBN-13 / EAN: 9780198534907
• Binding: Hardcover

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Product Description:

Recent work by mathematicians and physicists has uncovered revelatory connections between knot theory and the problem of developing a quantum theory of gravity. This book, the proceedings of a workshop held to bring together researchers in knot theory and quantum gravity, features a number of
expository and research papers that will aid significantly in closing the gap between the two disciplines. It will serve as a guide for mathematicians and physicists seeking to understand this rapidly developing area of research. The book represents a state-of-the-art study of current research and
progress. The editor is the author of Gauge Fields, Knots, and Gravity (World Scientific), a graduate level text on the topic.​

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Knot Theory: Proceedings, Plans-sur Bex, Switzerland 1977 (Lecture Notes in Mathematics)
By J. C. Hausmann

• Publisher: Springer
• Number Of Pages: 320
• Publication Date: 1978-11-15
• ISBN-10 / ASIN: 3540089527
• ISBN-13 / EAN: 9783540089520
• Binding: Paperback

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Linknot: Knot Theory by Computer (Series on Knots and Everything) (Series on Knots and Everything)
By Slavik Jablan, Radmila Sazdanovic

• Publisher: World Scientific Publishing Company
• Number Of Pages: 500
• Publication Date: 2007-11-16
• ISBN-10 / ASIN: 9812772235
• ISBN-13 / EAN: 9789812772237
• Binding: Hardcover

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Product Description:

LinKnot Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics. The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves. Hands-on computations using Mathematica or the webMathematica package LinKnot and beautiful illustrations facilitate better learning and understanding. LinKnot is also a powerful research tool for experimental mathematics implementation of Caudron's ideas. The use of Conway notation enables experimenting with large families of knots and links. Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata.​

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Knot Theory and Manifolds: Proceedings of a Conference held in Vancouver, Canada, June 2-4, 1983 (Lecture Notes in Mathematics)
By Dale Rolfsen

• Publisher: Springer
• Number Of Pages: 168
• Publication Date: 1985-10-25
• ISBN-10 / ASIN: 3540156801
• ISBN-13 / EAN: 9783540156802
• Binding: Paperback

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Knots and Physics
By Louis H. Kauffman

• Publisher: World Scientific Publishing Company
• Number Of Pages: 750
• Publication Date: 2001-12-15
• ISBN-10 / ASIN: 9810241127
• ISBN-13 / EAN: 9789810241124
• Binding: Paperback

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Product Description:

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.​

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An Introduction to Knot Theory (Graduate Texts in Mathematics)
By W.B.Raymond Lickorish

• Publisher: Springer
• Number Of Pages: 220
• Publication Date: 1997-10-03
• ISBN-10 / ASIN: 038798254X
• ISBN-13 / EAN: 9780387982540
• Binding: Hardcover

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Product Description:

This volume is an introduction to mathematical Knot Theory; the theory of knots and links of simple closed curves in three-dimensional space. It consists of a selection of topics which graduate students have found to be a successful introduction to the field. Three distinct techniques are employed; Geometric Topology Manoeuvres, Combinatorics, and Algebraic Topology. Each topic is developed until significant results are achieved and chapters end with exercises and brief accounts of state-of-the-art 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 twentienth 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 understandable style. Thus this constitutes a comprehensive introduction to the field, presenting modern developments in the context of classical material. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory although explanations throughout the text are plentiful and well-done. Written by an internationally known expert in the field, this volume will appeal to graduate students, mathematicians and physicists with a mathematical background who wish to gain new insights in this area.​

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The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
By Colin Conrad Adams

• Publisher: W.H. Freeman & Company
• Number Of Pages: 306
• Publication Date: 1994-03
• ISBN-10 / ASIN: 071672393X
• ISBN-13 / EAN: 9780716723936
• Binding: Hardcover

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Product Description:

Over a century old, knot theory is today one of the most active areas of modern mathematics. The study of knots has led to important applications in DNA research and the synthesis of new molecules, and has had a significant impact on statistical mechanics and quantum field theory.

Colin Adams’s The Knot Book is the first book to make cutting-edge research in knot theory accessible to a non-specialist audience. Starting with the simplest knots, Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians can now solve, as well as those that remain open. He also explores how knot theory is providing important insights in biology, chemistry, physics, and other fields. The new paperback edition has been updated to include the latest research results, and includes hundreds of illustrations of knots, as well as worked examples, exercises and problems.

With a simple piece of string, an elementary mathematical background, and The Knot Book, anyone can start learning about some of the most advanced ideas in contemporary mathematics.
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Amazon.com Review:

In February 2001, scientists at the Department of Energy's Los Alamos National Laboratory announced that they had recorded a simple knot untying itself. Crafted from a chain of nickel-plated steel balls connected by thin metal rods, the three-crossing knot stretched, wiggled, and bent its way out of its predicament--a neat trick worthy of an inorganic Houdini, but more than that, a critical discovery in how granular and filamentary materials such as strands of DNA and polymers entangle and enfold themselves.
A knot seems a simple, everyday thing, at least to anyone who wears laced shoes or uses a corded telephone. In the mathematical discipline known as topology, however, knots are anything but simple: at 16 crossings of a "closed curve in space that does not intersect itself anywhere," a knot can take one of 1,388,705 permutations, and more are possible. All this thrills mathematics professor Colin Adams, whose primer offers an engaging if challenging introduction to the mysterious, often unproven, but, he suggests, ultimately knowable nature of knots of all kinds--whether nontrivial, satellite, torus, cable, or hyperbolic. As perhaps befits its subject, Adams's prose is sometimes, well, tangled ("a knot is amphicheiral if it can be deformed through space to the knot obtained by changing every crossing in the projection of the knot to the opposite crossing"), but his book is great fun for puzzle and magic buffs, and a useful reference for students of knot theory and other aspects of higher mathematics. --Gregory McNamee​

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New Developments in the Theory of Knots (Advanced Series in Mathematical Physics, Vol. 11)
By Toshitake Kohno

• Publisher: World Scientific Pub Co Inc
• Number Of Pages: 800
• Publication Date: 1990-12
• ISBN-10 / ASIN: 9810201621
• ISBN-13 / EAN: 9789810201623
• Binding: Hardcover

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On Knots. (AM-115)
By Louis H. Kauffman

• Publisher: Princeton University Press
• Number Of Pages: 498
• Publication Date: 1987-10-01
• ISBN-10 / ASIN: 0691084351
• ISBN-13 / EAN: 9780691084350
• Binding: Paperback

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Summary: A good reference/second book on knot theory
Rating: 4

I don't feel that this book would be the best systematic introduction to the subject (say, for a course on knot theory). However, once someone has been introduced to knot theory(say, via a topology of manifolds class, more elementary book such as Adams, Livingston, or even a more advanced book such as Zieshang-Burde, Lickorish or Rolfsen), this book is an excellent reference.
The strength of this book is the "hands on" explinations given about many of the standard topics on knot theory (Alexander polynomial, Skein invariants, covering spaces, etc.) and I feel that the author does a great job on relating many of the combinatorial invariants to the topology of the knot complement. Many informative illustrations and examples are provided. This is one of the first references I look to when I need a refresher on a topic, or if I encounter something in classical knot theory that I am unfamiliar with.
Also, this book is just plain fun to read!
Of course, this book is from the mid 80's and therefore does not cover some of the more modern material.
Frankly, I've found that anything written by professor Kauffman to be well written and worth reading.​

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Knots, Groups and 3-Manifolds: Papers Dedicated to the Memory of R.H. Fox. (AM-84) (Annals of Mathematics Studies)
By Lee Paul Neuwirth

• Publisher: Princeton University Press
• Number Of Pages: 346
• Publication Date: 1975-08-01
• ISBN-10 / ASIN: 0691081700
• ISBN-13 / EAN: 9780691081700
• Binding: Hardcover

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