By Louis H. Kauffman
This publication deals a self-contained account of the 3-manifold invariants bobbing up from the unique Jones polynomial. those are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. ranging from the Kauffman bracket version for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of hyperlinks are built and mixed to shape the 3-manifold invariants. The tools during this publication are according to a recoupling conception for the Temperley-Lieb algebra. This recoupling idea is a q-deformation of the SU(2) spin networks of Roger Penrose.
The recoupling conception is built in a in simple terms combinatorial and common demeanour. Calculations are according to a reformulation of the Kirillov-Reshetikhin shadow international, resulting in expressions for the entire invariants when it comes to country summations on 2-cell complexes. large tables of the invariants are incorporated. Manifolds in those tables are well-known by means of surgical procedure shows and through 3-gems (graph encoded 3-manifolds) in an method pioneered by means of Sostenes Lins. The appendices comprise information regarding gem stones, examples of certain manifolds with a similar invariants, and functions to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.