Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134

This is a self-contained account of the 3-manifold invariants arising from the original Jones polynomial.

These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants.

Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants.

The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra.

This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose.