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

This book offers 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.

The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) 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 Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.

Author: Louis H. Kauffman, Sostenes Lins
Publisher: Princeton University Press
Published: 07/25/1994
Pages: 312
Binding Type: Paperback
Weight: 0.90lbs
Size: 9.23h x 6.11w x 0.78d
ISBN: 9780691036403

About the Author
Louis H. Kauffman is Professor of Mathematics at the University of Illinois, Chicago. Sostenes Lins is Professor of Mathematics at the Universidade Federal de Pernambuco in Recife, Brazil.