  We investigate the superconducting instability of a two-dimensional repulsive
fermion gas with Rashba spin-orbit coupling $\al_R$. Using renormalization
group approach, we find the superconducting transition temperature as a
function of the dimensionless ratio $\Theta={1}{2}m\al_R^2/E_F$ where $E_F=0$
when the smaller Fermi surface shrinks to a (Dirac) point. The general trend is
that superconductivity is enhanced as $\Theta$ increases, but in an
intermediate regime $\Theta\sim0.1$, a dome-like behavior appears. At a very
small value of $\Theta$, the angular momentum channel $j_z$ in which
superconductivity occurs is quite high. With increasing $\Theta$, $j_z$
decreases with a step of 2 down to $j_z=6$, after which we find the sequence
$j_z=6, 4, 6, 2$, the last value of which continues to
$\Theta\rightarrow\infty$. In an extended range of $\Theta$, the
superconducting gap predominantly resides on the large Fermi surface, while
Josephson coupling induces a much smaller gap on the small Fermi surface. Below
the superconducting transition temperature, we apply mean field theory to
derive the self-consistent equations and find the condensation energies. The
state with the lowest condensation energy is an unconventional superconducting
state which breaks time reversal symmetry, and in which singlet and triplet
pairings are mixed. In general, these states are topologically nontrivial, and
the Chern number of the state with total angular momentum $j_z$ is $C=2j_z$.
