  Spin fluctuations enter the calculation of the superconducting transition
temperature T$_c$ only in the next-to-leading order (i.e., in O(1/N$^2$) of the
1/N expansion of the t-J model. We have calculated these terms and show that
they have only little influence on the value of T$_c$ obtained in the leading
order O(1/N) in the optimal and overdoped region, i.e., for dopings larger than
the instability towards a flux phase. This result disagrees with recent
spin-fluctuation mediated pairing theories. The discrepancies can be traced
back to the fact that in our case the coupling between electrons and spins is
determined by the t-J model and not adjusted and that the spin susceptibility
is rather broad and structureless and not strongly peaked at low energies as in
spin-fluctuation models. Relating T$_c$ and transport we show that the
effective interactions in the particle-particle and particle-hole channels are
not simply related within the 1/N expansion by different Fermi surface averages
of the same interactin as in the case of phonons or spin fluctuations. As a
result, we find that large values for T$_c$ and rather small scattering rates
in the normal state as found in the experiments can easily be reconciled with
each other. We also show that correlation effects heavily suppress transport
relaxation rates relative to quasiparticle relaxation rates in the case of
phonons but not in the case of spin fluctuations.
