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

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


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About the Book

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.


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.


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Product Details
  • ISBN-13: 9780691036403
  • Publisher: Princeton University Press
  • Publisher Imprint: Princeton University Press
  • Depth: 19
  • Language: English
  • Returnable: Y
  • Spine Width: 20 mm
  • Width: 155 mm
  • ISBN-10: 0691036403
  • Publisher Date: 25 Jul 1994
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 312
  • Series Title: Annals of Mathematics Studies
  • Weight: 458 gr


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