  We consider the 3-manifold invariant I(M) which is defined by means of the
Chern-Simons quantum field theory and which coincides with the
Reshetikhin-Turaev invariant. We present some arguments and numerical results
supporting the conjecture that, for nonvanishing I(M), the absolute value |
I(M) | only depends on the fundamental group \pi_1 (M) of the manifold M. For
lens spaces, the conjecture is proved when the gauge group is SU(2). In the
case in which the gauge group is SU(3), we present numerical computations
confirming the conjecture.
