- The geometry and physics of knots – Atiyah M.

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• Annotation
• Contents
• Preface
• 1. History and background
• 1.1 General introduction
• 1.2 Gauge theories
• 1.3 History of knot theory
• 1.4 The Jones polynomial
• 2. Topological quantum field theories
• 2.1 Axioms for a topological QFT
• 2.2 Functions
• 3. Non-abelian moduli spaces
• 3.1 Moduli spaces of representations
• 3.2 Moduli spaces of holomorphic bundles
• 4 Symplectic quotients
• 4.1 Geometric invariant theory
• 4.2 Symplectic quotients
• 4.3 Quantization
• 4.4 Co-adjoint orbits
• 5 The infinite-dimensional case
• 5.1 Connections on Riemann surfaces
• 5.2 Marked points
• 5.3 Boundary components
• 6 Projective flatness
• 6.1 The direct approach
• 6.2 Conformai field theory
• 6.3 Abelianization
• 6.4 Degeneration of curves
• 7 The Feynman integral formulation
• 7.1 The Chern-Simons Lagrangian
• 7.2 Stationary-phase approximations
• 7.3 The Hamiltonian formulation
• 8. Final comments
• 8.1 Vacuum vectors
• 8.2 Skein relations
• 8.3 Surgery formula
• 8.4 Outstanding problems
• 8.5 Disconnected Lie groups
• References

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