We give an efficient parametrization of the set of boundary-unipotent representations of a 3-manifold group into SL(n,C), and use it to give a concrete formula for the Chern-Simons invariant. Numerical computations suggest that the imaginary part of the Chern-Simons invariant is always an integral linear combination of volumes of hyperbolic 3-manifolds. The talk will mostly deal with the case n=2, and Thurston's gluing equations.
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