By Louis H. Kauffman
This ebook deals a self-contained account of the 3-manifold invariants bobbing up from the unique Jones polynomial. those are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. ranging from the Kauffman bracket version for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of hyperlinks are developed and mixed to shape the 3-manifold invariants. The tools during this ebook are according to a recoupling thought for the Temperley-Lieb algebra. This recoupling thought is a q-deformation of the SU(2) spin networks of Roger Penrose.
The recoupling concept is built in a only combinatorial and easy demeanour. Calculations are in keeping with a reformulation of the Kirillov-Reshetikhin shadow international, resulting in expressions for the entire invariants by way of country summations on 2-cell complexes. huge tables of the invariants are incorporated. Manifolds in those tables are well-known via surgical procedure displays and by way of 3-gems (graph encoded 3-manifolds) in an process pioneered by way of Sostenes Lins. The appendices contain information regarding gem stones, examples of precise manifolds with an identical invariants, and purposes to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.
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