By Louis H. Kauffman
This ebook deals a self-contained account of the 3-manifold invariants coming 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 e-book are according to a recoupling concept for the Temperley-Lieb algebra. This recoupling idea is a q-deformation of the SU(2) spin networks of Roger Penrose.
The recoupling conception is built in a only combinatorial and trouble-free demeanour. Calculations are according to a reformulation of the Kirillov-Reshetikhin shadow global, resulting in expressions for all of the invariants by way of country summations on 2-cell complexes. large tables of the invariants are incorporated. Manifolds in those tables are famous through surgical procedure shows and through 3-gems (graph encoded 3-manifolds) in an strategy pioneered by means of Sostenes Lins. The appendices contain information regarding gem stones, examples of specific 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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