  The purpose of this paper is to generalize a theorem of Segal from [Seg79]
proving that the space of holomorphic maps from a Riemann surface to a complex
projective space is homology equivalent to the corresponding space of
continuous maps through a range of dimensions increasing with degree. We will
address if a similar result holds when other almost complex structures are put
on a projective space. For any compatible almost complex structure J on CP^2,
we prove that the inclusion map from the space of J-holomorphic maps to the
space of continuous maps induces a homology surjection through a range of
dimensions tending to infinity with degree. The proof involves comparing the
scanning map of topological chiral homology [Lur09], [And10], [Mil12]) with
analytic gluing maps for J-holomorphic curves ([MS94], [Sik03]). This is an
extension of the work done in [Mil11] regarding genus zero case.
