By Louis H. Kauffman

This booklet bargains 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 publication are in response to a recoupling idea for the Temperley-Lieb algebra. This recoupling conception is a q-deformation of the SU(2) spin networks of Roger Penrose.

The recoupling idea is constructed in a basically combinatorial and effortless demeanour. Calculations are in line with a reformulation of the Kirillov-Reshetikhin shadow global, resulting in expressions for all of the invariants when it comes to nation summations on 2-cell complexes. vast tables of the invariants are incorporated. Manifolds in those tables are well-known through surgical procedure displays and via 3-gems (graph encoded 3-manifolds) in an method pioneered through Sostenes Lins. The appendices contain information regarding gemstones, examples of specified manifolds with a similar invariants, and purposes to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.

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