  We show that the fundamental group of every enumeratively rationally
connected closed symplectic manifold is finite. In other words, if a closed
symplectic manifold has a non-zero Gromov-Witten invariant with two point
insertions, then it has finite fundamental group. We also show that if the
spherical homology class associated to such a non-zero Gromov-Witten invariant
is holomorphically indecomposable, then the rational second homology of the
symplectic manifold has rank one.
