Chern-Simons theory on an arbitrary manifold via surgery

Abstract

A general formula for physical observables in Chern-Simons theory with an arbitrary compact Lie group $G$, on an arbitrary closed oriented three-dimensional manifold $\cM$ is derived in terms of vacuum expectation values of Wilson loops in ${\cal S}^3$. Surgery presentation of $\cM$ and the Kirby moves are implemented as the main ingredients of the approach. The case of $G={\rm SU}(n)$ is explicitly calculated.