Quantum Invariants

Readers get a full, self-contained account of quantum invariants for knots and 3-manifolds. The book builds familiar knot polynomials, including the Jones and Alexander polynomials, as quantum invariants, drawing on representations of quantum groups and on the monodromy of solutions to the Knizhnik-Zamolodchikov equation.

The author then shows how the Kontsevich invariant and the theory of Vassiliev invariants bring order to this material. Topics include quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds.

The physical side is also covered. The text explains the Chern-Simons field theory and the Wess-Zumino-Witten model as the background against which these invariants arise.