3 problems

Torus theorem. Either $M$ contains an incompressible torus, or $M$ is a small Seifert fibre space.

Centre conjecture. Then $M$ is a Seifert fibre space.

Let $X$ be a symplectic $4$-manifold and let $\pi:X\rightarrow Y$ be a Seifert fibration. A fibered $3$-manifold is a $3$-manifold admitting a fibration over ${\mathbb S}^1$. Sympl…