CHERN-SIMONS INVARIANTS OF 3-MANIFOLDS DECOMPOSED ALONG TORI AND THE CIRCLE BUNDLE OVER THE REPRESENTATION SPACE OF T(2)

We describe a cut-and-paste method for computing Chem-Simons invariant of flat G-connections on 3-manifolds decomposed along tori, especially for G = SU(2) and SL(2,C). We use this method to make computations of SU(2) Chern-Simons invariants of graph manifolds which generalize Fintushel and Stern's computations for Seifert-fibered spaces. We also use this technique to give a simple derivation of a formula of Yoshida relating the flat SL(2, C) Chern-Simons invariant of the holonomy representation to the volume and the metric Chern-Simons invariant for cusped hyperbolic 3-manifolds.