## Rationally connected 3-folds and symplectic geometry Claire Voisin, Jussieu and IHES

We show that if $X$ is a rationally connected 3-fold which either is Fano or has $b_2(X)\leq 2$, and $Y$ is a compact Kaehler 3-fold symplectically equivalent to $X$, then $Y$ is also rationally connected.