Computer tests of Witten’s Chern-Simons theory against the theory of three-manifolds

We study Witten’s (2+1)-dimensional Chern-Simons theory with gauge group SU(2). The partition function in this theory is a topological invariant of three-manifolds. Following the prescription given by Witten, we explicitly calculate this partition function on some three-manifolds and verify many of the predictions made by the path integral. Most strikingly, we check the perturbation theory against the exact solution.