Hi. I have a question.
When X is a symplectic manifold which is diffeomorphic to T2-bundle over T2n, then does the first Chern class c1(X) vanishes in H2(X;R)? (i.e. a symplectic Calabi Yau)
Or, is there any example of T2-bundle over T2n which is not symplectic Calabi-Yau?
In fact, I proved that some 6-dimensional compact symplectic manifold M is symplectic Calabi-Yau, and M admits a T2-bundle structure over T4. But the proof is not pretty (the computation is really awful). So, I am worry about that my question might be true..
Thank you in advance.