Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 / Annals of Mathematics Studies Bd.134 (PDF)
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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.
- Autoren: Louis H. Kauffman , Sostenes Lins
- 2016, 312 Seiten, Englisch
- Verlag: Bonnier Books UK
- ISBN-10: 1400882532
- ISBN-13: 9781400882533
- Erscheinungsdatum: 02.03.2016
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- Größe: 4.64 MB
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