TemperleyLieb Recoupling Theory and Invariants of 3Manifolds (AM134) 
This book offers a selfcontained account of the 3manifold invariants arising from the original Jones polynomial. These are the WittenReshetikhinTuraev and the TuraevViro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic TemperleyLieb algebra, higherorder polynomial invariants of links are constructed and combined to form the 3manifold invariants. The methods in this book are based on a recoupling theory for the TemperleyLieb algebra. This recoupling theory is a qdeformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the KirillovReshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3gems (graph encoded 3manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the TuraevViro invariant and to the CraneYetter invariant of 4manifolds. "This extremely useful volume provides a selfcontained treatment of the construction of 3manifold invariants directly from the combinatorics of the Jones polynomial in Kauffman's bracket formulation."Mathematical Reviews Another Princeton book authored or coauthored by Louis H. Kauffman: Series:
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