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The 85 Ways to Tie a Tie: The Science and Aesthetics of Tie Knots
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Thomas Fink, Yong Mao
Paul Smith stylishness collides with Einsteinian precision when, bored with waiting for the next sartorial breakthrough in male fashion, two physicists prove that there are not just four ways to tie a tie, but a further 81. Tie Knots unravels the history of ties, the story of the discovery of the new knots and some very elegant mathematics in ...
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On Knots
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Louis H Kauffman
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Loops, knots, gauge theories and quantum gravity
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Gambini, Pullin
Now in paperback, this text provides a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. Loop representations (and the related topic of knot theory) are of considerable current interest because they provide a unified arena for the study of the gauge invariant quantization ...
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Noeuds: Genese D'Une Theorie Mathematique
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Alexei Sossinsky, Giselle Weiss (Translator), A B Sosinskii
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 ...
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Knots and Links
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Peter R Cromwell
Knots and links are studied by mathematicians, and are also finding increasing application in chemistry and biology. Many naturally occurring questions are often simple to state, yet finding the answers may require ideas from the forefront of research. This readable and richly illustrated book explores selected topics in depth in a way that makes ...
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An Introduction to Knot Theory
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W B Raymond Lickorish
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 ...
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High-Dimensional Knot Theory
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Andrew Ranicki
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 ...
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Knot Groups
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L. P. Neuwirth
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When Topology Meets Chemistry: A Topological Look at Molecular Chirality
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Erica Flapan, Ronald Graham (Editor), John Barrow (Editor)
The applications of topological techniques for understanding molecular structures have become increasingly important over the past thirty years. In this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, while learning the role these play in understanding molecular structures. Most ...
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Knot Theory
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Charles Livingston
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 ...
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Knots and Feynman Diagrams
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Dirk Kreimer, Peter Goddard (Editor), Julia Yeomans (Editor)
This book provides an accessible and up-to-date introduction to how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. Beginning with a summary of key ideas from perturbative quantum field theory and an introduction to the Hopf algebra structure of renormalization, early chapters discuss the rationality of ...
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Gauss Diagram Invariants for Knots and Links
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by
Thomas Fiedler
This book contains new numerical isotopy invariants for knots in the product of a surface (not necessarily orientable) with a line and for links in 3-space. These invariants, called Gauss diagram invariants, are defined in a combinatorial way using knot diagrams. The natural notion of global knots is introduced. Global knots generalize closed ...
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The Geometry and Physics of Knots
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Michael Francis Atiyah
These notes arise from lectures presented in Florence under the auspices of the Accadamia dei Lincee and deal with an area that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum ...
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Knots and Surfaces
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N D Gilbert, T Porter
Covering an area of current intense research interest, this book is ideal for all mathematicians, undergraduate or at research level, as an introduction to the field. The book provides a thorough account of the mathematical theory of knots and its interactions with related fields. This new paperback edition places the book within reach of all ...
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Knots & Physics
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by
Louis H. Kauffman
This book is an introduction to 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 framework, create a context that naturally includes a wide range of interrelated topics in topology and mathematical physics. The author takes ...
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Braids, Links, and Mapping Class Groups. (Am-82)
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Joan S Birman
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New Scientific Applications of Geometry and Topology
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by
De Witt L Sumners
Geometry and topology are subjects generally considered to be 'pure' mathematics. Recently, however, some of the methods and results in these two areas have found new utility in both wet-lab science (biology and chemistry) and theoretical physics. Conversely, science is influencing mathematics, from posing questions that call for the construction ...
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Symmetric Bends: How to Join Two Lengths
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by
Roger E Miles
A bend is a knot securely joining together two lengths of cord (or string or rope), thereby yielding a single longer length. There are many possible different bends, and a natural question that has probably occurred to many is: is there a "best" bend and, if so, what is it?" Most of the well-known bends happen to be symmetric - that is, the two ...
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Knot Theory & Its Applications
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by
Kunio Murasugi
Knot theory is a concept in algebraic topology that has found applications to a variety of mathematical problems as well as to problems in computer science, biological and medical research, and mathematical physics. This book is directed to a broad audience of researchers, beginning graduate students, and senior undergraduate students in these ...
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Classical Circuit Theory
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Jerome P Levine, Omar Wing
This book begins with the basic principles of circuits, derives their analytic properties in both the time and frequency domains, and states and proves the two important theorems. It then develops an algorithmic method to design common and uncommon types of circuits, such as prototype filters, lumped delay lines, constant phase difference circuits ...
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Knot Book
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by
Colin C. Adams
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 it is having a significant impact on statistical mechanics and quantum field theory. Many of the problems discussed in knot theory, including those ...
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Formal Knot Theory
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Louis H Kauffman
This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author 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. 1983 edition. Includes 51 ...
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Knots, Groups, and 3-Manifolds: Papers Dedicated to the Memory of R. H. Fox
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L. P. Neuwirth
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Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds
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Louis H Kauffman, Louis H Kaufmann, Sosteness Lins
This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are ...
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Knots and Surfaces: A Guide to Discovering Mathematics
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by
David W Farmer
In most mathematics textbooks, the most exciting part of mathematics - the process of invention and discovery - is completely hidden from the reader. The aim of "Knots and Surfaces" is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; ...
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