To pinpoint the microscopic mechanism for superconductivity has
proven to be one of the most outstanding challenges in the physics of
correlated quantum matter. Thus far, the most direct evidence for
an electronic pairing mechanism is the observation of a new symmetry
of the order-parameter, as done in the cuprate high-temperature
superconductors. Like distinctions based on the symmetry of a locally
defi�ned order-parameter, global, topological invariants allow for
a sharp discrimination between states of matter that cannot be transformed
into each other adiabatically. Here we propose an unconventional
pairing state for the electron
uid in two-dimensional oxide
interfaces and establish a direct link to the emergence of nontrivial
topological invariants. Topological superconductivity and Majorana edge states can then be used to detect the microscopic origin for
superconductivity. In addition, we show that also the density wave
states that compete with superconductivity sensitively depend on the
nature of the pairing interaction. Our conclusion is based on the special
role played by the spin-orbit coupling and the shape of the Fermi
surface in SrTiO3/LaAlO3-interfaces and closely related systems.