Profinite rigidity and surface bundles over the circle

Martin R. Bridson, Alan W. Reid, Henry Wilton

If $M$ is a compact 3-manifold whose first betti number is 1, and $N$ is a compact 3-manifold such that ${\pi }_{1}N$ and ${\pi }_{1}M$ have the same finite quotients, then $M$ fibres over the c…