We study symplectic geometry of rationally connected 3-folds. The first
result shows that rationally connectedness is a symplectic deformation
invariant in dimension 3. If a rationally connected 3-fold X is Fano or
b2​(X)=2, we prove that it is symplectic rationally connected, i.e. there is
a non-zero Gromov-Witten invariant with two insertions being the class of a
point. Finally we prove that many rationally connected 3-folds are birational
to a symplectic rationally connected variety.Comment: 25 pages. Preliminary version. Comments are welcom