Taubes's symplectic-fibration conjecture for 3-manifolds

Let $N$ be a $3$-manifold, and let $S^{1} \times N$ admit a symplectic structure $\omega$. Taubes's conjecture. Then $N$ admits a fibration over $S^{1}$. This conjecture relates symplectic structures on products $S^{1} \times N$ to fibredness of $N$; the source presents it as the central conjecture studied in the section, without stating a resolution.