2 problems

Symplecticity conjecture. For sufficiently large $k$, the transverse hyperplane sections of $F_k$ are symplectic submanifolds of $X$.

Let $(M^{2n},\omega)$ be a compact symplectic manifold. A class $\alpha\in H_{2k}(M^{2n},\mathbb Z)$ is formal symplectic when $\langle\alpha,\omega^k\rangle$ is positive, and it i…