Taubes' conjecture on symplectic products and fibred 3-manifolds

Let $M$ be a closed oriented 3--manifold. Taubes' conjecture. The product $S^1 \times M$ admits a symplectic structure if and only if $M$ fibers over $S^1$. The conjecture relates symplectic structures on products to fibred 3-manifolds and is presented in the source as the predecessor of Baldridge's conjecture; its resolution is not specified in the source.