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Preface to the Second Edition | p. vii |
Foreword to the First Edition | p. ix |
From the Introduction to the First Edition | p. xi |
Acknowledgments | p. xv |
Bernhard Riemann | p. 1 |
Beginnings | p. 3 |
Doctoral Dissertation | p. 11 |
Privatdozent at Göttingen | p. 23 |
Riemann and Dirichlet | p. 43 |
Full Professor in Göttingen | p. 63 |
Last Years | p. 75 |
Posthumous Fate | p. 77 |
Bibliography to Part I | p. 83 |
Topological Themes in Contemporary Physics | p. 85 |
Introduction | p. 89 |
Topological Structures | p. 95 |
The Connectivity of a Manifold and Quantization of Magnetic Flux | p. 107 |
Systems with Spontaneous Symmetry Breaking | p. 109 |
Topology and Liquid Crystals | p. 113 |
Theory of Gauge Fields | p. 127 |
Topological Particles | p. 145 |
Instantons, or Pseudo-Particles | p. 149 |
Soliton Particles | p. 157 |
Knots, Links, and Physics | p. 167 |
Von Neumann Algebras | p. 168 |
The Dimension of a Factor | p. 169 |
The Theory of Braids | p. 171 |
The Group of Braids | p. 172 |
The Skein Relations | p. 174 |
Condensed Matter Theory | p. 176 |
Example 1 | p. 177 |
Example 2 | p. 179 |
Magnetohydrodynamics | p. 179 |
What Next? | p. 183 |
The Quantum Hall Effect | p. 184 |
Quasicrystals | p. 185 |
Membranes | p. 188 |
A Brief Historical Survey | p. 191 |
Bibliography to Part II | p. 195 |
Index | p. 199 |
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