Knots and physics

Abstract

This paper traces the construction of the bracket model of the Jones polynomial, and how this model can be naturally interpreted as a vacuum-vacuum expectation in a combinatorial version of physical theory. From this point of view certain structures such as solutions to the Yang-Baxter equation, and the quantum group for $SL(2)$ emerge naturally from topological considerations. We then see how quantum groups give rise to invariants of links via solutions to the Yang-Baxter equation. Section 5, is an original treatment of the construction of the universal R-matrix. All the other material has, or will appear elsewhere in similar form.