Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134
Princeton, NJ: Princeton University Press, [2016]
Online
Monographie, Elektronische Ressource
- 1 online resource (312 p.) : 1200 illus
Ermittle Ausleihstatus...
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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Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134
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Verantwortlichkeitsangabe: | Sostenes Lins, Louis H. Kauffman |
Autor/in / Beteiligte Person: | Kauffman, Louis H. ; Lins, Sostenes |
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Veröffentlichung: | Princeton, NJ: Princeton University Press, [2016] |
Medientyp: | Monographie |
Datenträgertyp: | Elektronische Ressource |
Umfang: | 1 online resource (312 p.) : 1200 illus |
ISBN: | 9781400882533 |
DOI: | 10.1515/9781400882533 |
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