  In a well known work [Se], Graeme Segal proved that the space of holomorphic
maps from a Riemann surface to a complex projective space is homology
equivalent to the corresponding continuous mapping space through a range of
dimensions increasing with degree. In this paper, we address if a similar
result holds when other (not necessarily integrable) almost complex structures
are put on projective space. We take almost complex structures that are
compatible with the underlying symplectic structure. We obtain the following
result: the inclusion of the space of based degree k J-holomorphic maps from
P^1 to P^2 into the double loop space of P^2 is a homology surjection for
dimensions j<3k-2. The proof involves constructing a gluing map analytically in
a way similar to McDuff and Salamon in [MS] and Sikorav in [S] and then
comparing it to a combinatorial gluing map studied by Cohen, Cohen, Mann, and
Milgram in [CCMM].
