Louis H. Kauffman, Sostenes Lins

Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Bonnier Books UK
• Seitenzahl: 312
• Erscheinungstermin: 2. März 2016
• Englisch
• ISBN-13: 9781400882533
• Artikelnr.: 45987281

Autorenporträt

Louis H. Kauffman & Sostenes Lins

Inhaltsangabe

1
Introduction
1
2
Bracket Polynomial, Temperley-Lieb Algebra
5
3
Jones-Wenzl Projectors
13
4
The 3-Vertex
22
5
Properties of Projectors and 3-Vertices
36
6
[theta]--Evaluations
45
7
Recoupling Theory Via Temperley-Lieb Algebra
60
8
Chromatic Evaluations and the Tetrahedron
76
9
A Summary of Recoupling Theory
93
10
A 3-Manifold Invariant by State Summation
102
11
The Shadow World
114
12
The Witten-Reshetikhin-Turaev Invariant
129
13
Blinks [actual symbol not reproducible] 3-Gems: Recognizing 3-Manifolds
160
14
Tables of Quantum Invariants
185
Bibliography
290
Index
295

Rezensionen

This extremely useful volume provides a self-contained treatment of the construction of 3-manifold invariants directly from the combinatorics of the Jones polynomial in Kauffman's bracket formulation.