  We analyze the possible interaction-induced superconducting instabilities in
noncentrosymmetric systems based on symmetries of the normal state. It is
proven that pure electron-phonon coupling will always lead to a fully gapped
superconductor that does not break time-reversal symmetry and is topologically
trivial. We show that topologically nontrivial behavior can be induced by
magnetic doping without gapping out the resulting Kramers pair of Majorana edge
modes. In case of superconductivity arising from the particle-hole fluctuations
associated with a competing instability, the properties of the condensate
crucially depend on the time-reversal behavior of the order parameter of the
competing instability. When the order parameter preserves time-reversal
symmetry, we obtain exactly the same properties as in case of phonons. If it is
odd under time-reversal, the Cooper channel of the interaction will be fully
repulsive leading to sign changes of the gap and making spontaneous
time-reversal symmetry breaking possible. To discuss topological properties, we
focus on fully gapped time-reversal symmetric superconductors and derive
constraints on possible pairing states that yield necessary conditions for the
emergence of topologically nontrivial superconductivity. These conditions might
serve as a tool in the search for topological superconductors. We also discuss
implications for oxides heterostructures and single-layer FeSe.
