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| Preface to the First Edition | |
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| Preface to the Second Edition | |
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| Preface to the Third Edition | |
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| Preface to the Fourth Edition | |
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| A Short Course of Knots and Physics | |
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| Physical Knots | |
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| Diagrams and Moves | |
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| States and the Bracket Polynomial | |
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| Alternating Links and Checkerboard Surfaces | |
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| The Jones Polynomial and its Generalizations | |
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| An Oriented State Model for V<sub>K</sub>(t) | |
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| Braids and the Jones Polynomial | |
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| Abstract Tensors and the Yang-Baxter Equation | |
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| Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)<sub>q</sub> | |
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| The Form of the Universal R-matrix | |
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| Yang-Baxter Models for Specializations of the Homily Polynomial | |
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| The Alexander Polynomial | |
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| Knot-Crystals - Classical Knot Theory in a Modern Guise | |
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| The Kauffman Polynomial | |
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| Oriented Models and Piecewise Linear Models | |
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| Three Manifold Invariants from the Jones Polynomial | |
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| Integral Heuristics and Witten's Invariants | |
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| Appendix - Solutions to the Yang-Baxter Equation | |
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| Knots and Physics - Miscellany | |
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| Theory of Hitches | |
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| The Rubber Band and Twisted Tube | |
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| On a Crossing | |
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| Slide Equivalence | |
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| Unoriented Diagrams and Linking Numbers | |
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| The Penrose Chromatic Recursion | |
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| The Chromatic Polynomial | |
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| The Potts Model and the Dichromatic Polynomial | |
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| Preliminaries for Quantum Mechanics, Spin Networks and Angular Momentum | |
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| Quaternions, Cayley Numbers and the Belt Trick | |
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| The Quaternion Demonstrator | |
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| The Penrose Theory of Spin Networks | |
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| Q-Spin Networks and the Magic Weave | |
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| Knots and Strings - Knotted Strings | |
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| DNA and Quantum Field Theory | |
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| Knots in Dynamical Systems - The Lorenz Attractor | |
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| Coda | |
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| References | |
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| Appendix | |
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| Introduction | |
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| Gauss Codes, Quantum Groups and Ribbon Hopf Algebras | |
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| Spin Networks, Topology and Discrete Physics | |
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| Link Polynomials and a Graphical Calculus | |
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| Knots, Tangles, and Electrical Networks | |
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| Knot Theory and Functional Integration | |
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| Introduction to Virtual Knot Theory and Khovanov Homology | |
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| Index | |