Three-manifolds and the Temperley-Lieb algebra (Q1184147)

The bracket polynomial invariant due to Kauffman gave an exceedingly simple definition of the Jones polynomial invariant for links. That bracket polynomial is here manipulated via linear skein theory and interpreted via the discipline of the Temperley-Lieb algebra. Those techniques are then combined to give a short, direct proof, from first principles, of the existence of Witten's 3-manifold invariants that correspond to \(SU_ q(2)\), and of the associated invariants of links in 3-manifolds.