Temperley-Lieb Recoupling Theory and Invariants of 3-manifolds

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Princeton University Press, 1994 - Mathematics - 296 pages
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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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Contents

Bracket Polynomial TemperleyLieb Algebra
5
JonesWenzl Projectors
13
The 3Vertex
22
Properties of Projectors and 3Vertices
36
Evaluations
45
Recoupling Theory Via TernperleyLieb Algebra
60
Chromatic Evaluations and the Tetrahedron
76
A Summary of Recoupling Theory
93
A 3Manifold Invariant by State Summation
102
The Shadow World
114
The WittenReshetikhinTuraev Invariant
129
Recognizing 3Manifolds
160
Tables of Quantum Invariants
185
Bibliography
290
Copyright

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TEMPERLEY-LIEB RECOUPLING THEORY AND INVARIANTS OF 3-MANIFOLDS By ...
TEMPERLEY-LIEB RECOUPLING THEORY AND INVARIANTS OF 3-MANIFOLDS By Louis H. Kauffman and Sostenes L. Lins: 296 pp.,£ 40.00, ISBN 0 691 03640 3 (Princeton ...
journals.cambridge.org/ abstract_S0024609396211671

KNOTS by Louis H. Kauffman Abstract: This paper is an introduction ...
KNOTS. by Louis H. Kauffman. Abstract: This paper is an introduction to the landscape of knot theory and its relationships ...
math.uic.edu/ ~kauffman/ KNOTS.pdf

[ISI Highly Cited Researchers Version 1.5]
'Temperley-Lieb recoupling theory and invariants of 3-manifolds' by lh Kauffman and sl Lins Bull. London Math. Soc. 29 (1997) 109-127.. LICKORISH, WBR. ...
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Phys. Rev. Lett. 94, 057206 (2005): Nachtergaele and Starr ...
[13] lh Kauffman and sl Lins, Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (Princeton University Press, Princeton, NJ, 1994). ...
link.aps.org/ doi/ 10.1103/ PhysRevLett.94.057206

Kauffman, lh and Lins, S.: Temperley-Lieb Recoupling Theory and ...
Description of the book Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134) by Kauffman, LH and Lins, S., published by Princeton ...
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Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds, by Louis Kauffman and Sostenes Lins, to be published by Princeton U. Press. ...
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Kauffman, lh Lins, sl 134 Princeton University Press Temperley ...
Kauffman, lh Lins, sl 134 Princeton University Press Temperley–Lieb Recoupling Theory and Invariants of 3-Manifolds 1994 Annals of Mathematics Studies ...
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louis h kaufmann libri - I Libri dell'autore: Louis H Kaufmann ...
Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (Am-134) · Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (Am-134) ...
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About the author (1994)

Kauffman-University of Illinois, Chicago

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