Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation (Q1200076)

The study of the new invariants of 3-dimensional manifolds introduced by E. Witten using Chern-Simons gauge theory is performed for certain families of three-manifolds. Namely, explicit formulas for the Chern- Simons-Witten invariants of lens spaces and torus bundles over \(S^ 1\) are determined, for arbitrary values of the level \(k\), with emphasis on the group \(G=\text{SU}(2)\). The author exhibits explicitly the agreement of the limiting values of the derived formulas as \(k\to\infty\), with the semiclassical approximation predicted by the Chern-Simons path integral. An appendix of notations and preliminary results is also provided.