Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds
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Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds by Louis H. Kauffman
Book DescriptionThis 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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Book DetailsISBN: 9780691036403
(229mm x 152mm x 16mm)
Imprint: Princeton University Press
Publisher: Princeton University Press
Publish Date: 5-Jul-1994
Country of Publication: United States
Books By Author Louis H. Kauffman
Mereon Matrix, Hardback (May 2013)View all books by Louis H. Kauffman
Mereon is an approach to the unification of knowledge that relies on whole systems modelling. It is a scientific framework that charts the sequential, emergent growth process of systems. This book provides the fundamentals of such connections for an ongoing search for order, directionality, and diversity that is found in this unity.
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