Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134) - Louis H. Kauffman, Sostenes Lins, Lins, So´stenes (1994)
ISBN 0691036403
Subject Knot theory; Three-manifolds (Topology); Invariants
Publisher Princeton University Press
Publication Date 7/5/1994
Format Paperback (234 x 155 mm)
Language e

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.

Personal Details
Collection Status In Collection
Index 186
Read It Yes
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Product Details
LoC Classification QA612.2.K39 1994
Dewey 514/.224
Cover Price $67.50
No. of Pages 312