TEMPERLEY-LIEB RECOUPLING THEORY AND INVARIANTS OF 3-MANIFOLDS (AM-134), VOLUME 134 by Louis H. Kauffman, Sostenes Lins ( 9780691036403 )

Item Details

Title:

TEMPERLEY-LIEB RECOUPLING THEORY AND INVARIANTS OF 3-MANIFOLDS (AM-134), VOLUME 134

By:

Louis H. Kauffman, Sostenes Lins

Format:

Paperback

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£109.00

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£87.20

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ISBN 10:

0691036403

ISBN 13:

9780691036403

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Publisher:

PRINCETON UNIVERSITY PRESS

Pub. date:

5 July, 1994

Series:

Annals of Mathematics Studies 134

Pages:

312

Description:

Offers an account of the 3-manifold invariants arising from the original Jones polynomial. This book contains the methods that are based on a recoupling theory for the Temperley-Lieb algebra. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant.

Synopsis:

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.

Illustrations:

1200 illus.

Publication:

Imprint:

Princeton University Press

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Returnable

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COMBINATORIAL PHYSICS (HB)

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