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- DescriptionThis book offers a self-contained account of the 3-manifold invariants arising from the original Jones polymial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polymial and the diagrammatic Temperley-Lieb algebra, higher-order polymial 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.
- Author(s)Louis H. Kauffman,Sostenes Lins
- PublisherPrinceton University Press
- Date of Publication05/07/1994
- Series TitleAnnals of Mathematics Studies
- Series Part/Volume Numberv.134
- Place of PublicationNew Jersey
- Country of PublicationUnited States
- ImprintPrinceton University Press
- Content Note1200 illus.
- Weight428 g
- Width152 mm
- Height229 mm
- Spine16 mm
- Format DetailsTrade paperback (US)
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