  Using an asymptotically exact weak coupling analysis of a multi-orbital
Hubbard model of the electronic structure of \SRO, we show that the interplay
between spin and charge fluctuations leads unequivocally to triplet pairing
which originates in the quasi-one dimensional bands. The resulting
superconducting state spontaneously breaks time-reversal symmetry and is of the
form $\Delta \sim p_x + i p_y \hat{z}$ with sharp gap minima and a d-vector
that is only {\it weakly} pinned. The supercondutor is topologically {\it
trivial} and hence lacks robust chiral Majorana fermion modes along the
boundary. The absence of topologically protected edge modes could explain the
surprising absence of experimentally detectable edge currents in this system.
