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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 | |