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| Preface to the First Edition Preface to the Second Edition Preface to the Third Edition Part I. A Short Course of Knots and Physics 1. Physical Knots 2. Diagrams and Moves 3. States and the Bracket Polynomial 4. Alternating Links and Checkerboard Surfaces 5. The Jones Polynomial and its Generalizations 6. An Oriented State Model for VK(t) 7. Braids and the Jones Polynomial 8. Abstract Tensors and the Yang-Baxter Equation 9. Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)q 10. The Form of the Universal R-matrix 11. Yang-Baxter Models for Specializations of the Homily Polynomial .. 12. Tile Alexander Polynomial 13. Knot-Crystals - Classical Knot Theory in a Modern Guise 14. The Kauffman Polynomial 15. Oriented Models and Piecewise Linear Models 16. Three Manifold Invariants from the Jones Polynomial 17. Integral Heuristics and Witten's Invariants 18. Appendix - Solutions to the Yang-Baxter Equation Part II. Knots and Physics-Miscellany 1. Theory of Hitches 2. The Rubber Band and Twisted Tube 3. On a Crossing 4. Slide Equivalence 5. Unoriented Diagrams and Linking Numbers 6. The Penrose Chromatic Recursion 7. The Chromatic Polynomial 8. The Potts Model and the Dichrornatic Polynomial 9. Preliminaries for Quantum Mechanics, Spin Networks and Angular Momentum 10. Quaternions, Cayley Numbers and the Belt Trick 11. The Quaternion Demonstrator 12. The Penrose Theory of Spin Networks 13. Q-Spin Networks and the Magic Weave 14. Knots and Strings - Knotted Strings 15. DNA and Quantum Field Theory 16. Knots in Dynamical Systems - The Lorenz Attractor Coda References Index Appendix Introduction Gauss Codes, Quantum Groups and Ribbon Hopf Algebras Spin Networks, Topology and Discrete Physics Link Polynomials and a Graphical Calculus Knots, Tangles, and Electrical Networks Knot Theory and Functional Integration |
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