Topology and physics

Preface Early examples of topological concepts in physics......Page 6
Contents......Page 8
 1. Introduction......Page 10
 2. Topology and Physics of Algebraic Surfaces......Page 13
 3. Valley of Stability......Page 17
 4. Intersection Form......Page 19
 5. Other Surfaces......Page 21
 6. Conclusions......Page 23
 References......Page 24
Chapter 2 Developments in topological gravity......Page 26
 1. Introduction......Page 27
 2. Weil{Petersson Volumes and Two-Dimensional Topological Gravity......Page 28
 3. Open Topological Gravity......Page 39
 4. Interpretation via Matrix Models......Page 73
 References......Page 86
 1. Introduction......Page 90
 2. Braids......Page 94
 3. Braiding Operators and Universal Quantum Gates......Page 96
 4. Fermions, Majorana Fermions and Braiding Fermion Algebra.......Page 98
 6. Majorana Fermions Generate Universal Braiding Gates......Page 106
 7. The Bell-Basis Matrix and Majorana Fermions......Page 107
 References......Page 115
 1. Fermat's Principle......Page 118
 2. Diophantine Geometry and Gauge Theory......Page 119
 3. Principal Bundles and Number Theory: Weil's Constructions......Page 121
 4. Arithmetic Gauge Fields......Page 122
 Lemma 4.1.......Page 123
 5. Homotopy and Gauge Fields......Page 126
 6. The Local to Global Problem, Reciprocity Laws, and Euler Lagrange Equations......Page 129
 7. The Tate Shafarevich Group and Abelian Gauge Fields......Page 132
 8. Non-Abelian Gauge Fields and Diophantine Geometry......Page 134
 Conjecture 8.1 (Ref.6).......Page 136
 and Chern Simons Actions......Page 138
 References......Page 142
 5.1. General Background......Page 144
 5.2. The Big Bang and Gravitational Collapse......Page 147
 5.3. Collapse to a Black Hole......Page 149
 5.4. The Problem of Generic Gravitational Collapse......Page 153
 5.5. Causal Structure of Space-Times......Page 156
 5.6. Geodetic Maximality......Page 163
 5.7. Collapse to Singularity......Page 168
 Bibliography......Page 178
 1. Introduction......Page 182
 2. 2D Non-Abelian Objects......Page 183
 3. Three-Dimensional Topological Physics Beyond Anyons......Page 186
 4. Four-Dimensional Topological Physics......Page 187
 References......Page 189
 1. Four Revolutions in Physics......Page 190
 2. It From Qubit, Not Bit A Second Quantum Revolution......Page 198
 matter = information......Page 199
 Eight wonders:......Page 200
 3. A String-Net Liquid of Qubits and A Uni cation of Gauge Interactions and Fermi Statistics......Page 201
 References......Page 211
Appendix | SO4 symmetry in a Hubbard model......Page 224