Computer calculation of Witten's 3-manifold invariant

• DOI: 10.1007/bf02100006
• Publication Date: 2005-09-12T20:23:24Z
• Authors: Daniel S. Freed; Robert E. Gompf
• Keywords: Manifold (fluid mechanics); Finite type invariant

Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant.