  We present a scheme of interaction-induced topological bandstructures based
on the spin anisotropy of exciton-polaritons in semiconductor microcavities. We
predict theoretically that this scheme allows the engineering of topological
gaps, without requiring a magnetic field or strong spin-orbit interaction
(transverse electric-transverse magnetic splitting). Under non-resonant
pumping, we find that an initially topologically trivial system undergoes a
topological transition upon the spontaneous breaking of phase symmetry
associated with polariton condensation. Under resonant coherent pumping, we
find that it is also possible to engineer a topological dispersion that is
linear in wavevector -- a property associated with polariton superfluidity.
