Contents

Preface   ix

History and background         1

General introduction               1

Gauge theories       2

History of knot theory             5

The Jones polynomial             7

Topological quantum field theories         12

Axioms for a topological QFT 12

Canonical quantization            17

0-functions              19

Non-abelian moduli spaces    24

Moduli spaces of representations          24

 

 

Moduli spaces of holomorphic bundles  26

Symplectic quotients               30

Geometric invariant theory     30

Symplectic quotients               31

Quantization            33

Co-adjoint orbits      35

The infinite-dimensional case 37

Connections on Riemann Surfaces        37

Marked points         40

Boundary components           42

Projective flatness  45

The direct approach               45

Conformal field theory             46

Abelianization          47

Degeneration of curves          50The Feynman integral formulation      52

The Chern-Simons Lagrangian              52

Stationary-phase approximations           55

The Hamiltonian formulation   63

Final comments      66

Vacuum vectors     66

Skein relations        67

Surgery formula      69

Outstanding problems            70

Disconnected Lie groups        72 References        73 Index  77