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Computer Calculation of Witten's 3-Manifold Invariant

D. Freed
R. Gompf
Journal / Anthology

Communications in Mathematical Physics
Year: 1991
Volume: 141
Issue: 1
Page range: 79-117

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.

*Mathematics > Topology