| Preface to the First Edition |
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vii | |
| Preface to the Second Edition |
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xi | |
| Preface to the Third Edition |
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xiii | |
| Preface to the Fourth Edition |
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xv | |
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Part I A Short Course of Knots and Physics |
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4 | (4) |
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8 | (17) |
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3 States and the Bracket Polynomial |
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25 | (14) |
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4 Alternating Links and Checkerboard Surfaces |
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39 | (10) |
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5 The Jones Polynomial and its Generalizations |
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49 | (25) |
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6 An Oriented State Model for VK (t) |
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74 | (11) |
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7 Braids and the Jones Polynomial |
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85 | (19) |
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8 Abstract Tensors and the Yang-Baxter Equation |
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104 | (13) |
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9 Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)q |
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117 | (31) |
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10 The Form of the Universal R-matrix |
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148 | (13) |
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11 Yang-Baxter Models for Specializations of the Homfly Polynomial |
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161 | (13) |
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12 The Alexander Polynomial |
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174 | (12) |
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13 Knot-Crystals - Classical Knot Theory in a Modern Guise |
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186 | (29) |
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14 The Kauffman Polynomial |
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215 | (20) |
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15 Oriented Models and Piecewise Linear Models |
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235 | (15) |
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16 Three Manifold Invariants from the Jones Polynomial |
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250 | (35) |
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17 Integral Heuristics and Witten's Invariants |
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285 | (31) |
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18 Appendix - Solutions to the Yang-Baxter Equation |
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316 | (7) |
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Part II Knots and Physics --- Miscellany |
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323 | (6) |
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2 The Rubber Band and Twisted Tube |
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329 | (3) |
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332 | (4) |
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336 | (3) |
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5 Unoriented Diagrams and Linking Numbers |
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339 | (7) |
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6 The Penrose Chromatic Recursion |
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346 | (7) |
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7 The Chromatic Polynomial |
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353 | (11) |
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8 The Potts Model and the Dichromatic Polynomial |
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364 | (17) |
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9 Preliminaries for Quantum Mechanics, Spin Networks and Angular Momentum |
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381 | (22) |
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10 Quaternions, Cayley Numbers and the Belt Trick |
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403 | (24) |
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11 The Quaternion Demonstrator |
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427 | (16) |
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12 The Penrose Theory of Spin Networks |
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443 | (16) |
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13 Q-Spin Networks and the Magic Weave |
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459 | (16) |
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14 Knots and Strings - Knotted Strings |
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475 | (13) |
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15 DNA and Quantum Field Theory |
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488 | (13) |
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16 Knots in Dynamical Systems - The Lorenz Attractor |
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501 | (32) |
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511 | (2) |
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513 | (20) |
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533 | (10) |
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Gauss Codes, Quantum Groups and Ribbon Hopf Algebras |
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543 | (46) |
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Spin Networks, Topology and Discrete Physics |
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589 | (41) |
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Link Polynomials and a Graphical Calculus |
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630 | (46) |
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Knots, Tangles, and Electrical Networks |
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676 | (40) |
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Knot Theory and Functional Integration |
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716 | (47) |
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Introduction to Virtual Knot Theory and Khovanov Homology |
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763 | (72) |
| Index |
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835 | |