Chapter 1. Introduction
Quantum physics and classical electromagnetism, Abelian Chern-Simons
action, Non-Abelian Chern-Simons action
Chapter 2. Basic notions of knot theory
Ambient and regular isotopy, Link invariants, Framing and satellites
Chapter 3. Framing in field theory
Abelian Chern-Simons theory, Framed Wilson line operators
Chapter 4. Non-Abelian Chern-Simons theory
Covariant quantization, One-loop effective action, Higher order
results
Chapter 5. Observables and perturbation theory
Wilson line operators, Perturbative computations
Chapter 6. Properties of the expectation values
Holonomy matrix, Discrete symmetries, Satellite formulae
Chapter 7. Ordering fermions and knot observables
Ordering fermions, Antiperiodic boundary conditions, Knot observables
Chaper 8. Braid group
Artin braid group, Hecke algebra
Chapter 9. R-matrix and braids
Quantum group approach, Lie algebras and monodromy representations,
Quasi-Hopf algebra
Chapter 10. Chern-Simons monodromies
Schrödinger picture, Universality of the link invariants,
The inexistent shift
Chapter 11. Defining relations
Calculus rules
Chapter 12. The extended Jones polynomial
The values of the unknots, Hopf link, Trefoil knot, Figure-eight
knot, Connection with the Jones polynomial, Bracket connection,
Reconstruction theorems
Chapter 13. General properties
Twist variable, Recovered field theory, Links in a solid torus,
Satellites, Skein relation, Projectors, Borromean rings, Connected
sums, Mutations
Chapter 14. Unitary groups
Fundamental skein relation, Casimir operator, Composite states,
Pattern links, Higer dimensional representations, Polynomial structure,
SU(3) examples
Chapter 15. Reduced tensor algebra
The restated solution, Outlook, Representation ring, The three-sphere,
Reduced tensor algebra, Roots of unity, Special cases
Chapter 16. Surgery on three-manifolds
Mapping class group of the torus, Solid tori, Dehn surgery, Links
in three-manifolds, Elementary surgeries, Physical interpretation,
The fundamental group
Chapter 17. Surgery and field theory
Basic pairing, Properties of the Hopf matrix, Elementary surgery
operators, Surgery operator, Surgery rules and Kirby moves
Chapter 18. Observables in three-manifolds
The manifold S^1 x S^2 , The manifold RP^3 , Lens
spaces, The Poincaré manifold, The manifold T^2 x
S^1
Chapter 19. Three-manifold invariant
Improved partition function, Values of the invariant
Chapter 20. Abelian surgery invariant
Compact Abelian theory, Abelian surgery rules, Abelian surgery
invariant
References
Subject Index