  In this paper we continue our study on the moduli spaces of flat G-bundles,
for any semi-simple Lie group G, over a Riemann surface by using heat kernel
and Reidemeister torsion. Formulas for intersection numbers on the moduli
spaces over a Riemann surface with several boundary components, over
non-orientable Riemann surfaces are obtained. Some general vanishing theorems
about characteristic numbers of the moduli spaces are proved. We also extend
our method to study Higgs moduli spaces, to introduce invariants for knots and
3-manifolds.
