, Volume 121, Issue 3, pp 351-399

Quantum field theory and the Jones polynomial

Abstract

It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS 3 to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation. These results shed a surprising new light on conformal field theory in 1+1 dimensions.

An expanded version of a lecture at the IAMP Congress, Swansea, July, 1988
Research supported in part by NSF Grant No. 86-20266, and NSF Waterman Grant 88–17521
Communicated by A. Jaffe