  We prove that if $G$ fibres algebraically and is part of a
$\mathrm{PD}^3$-pair, then $G$ is the fundamental group of a fibred compact
aspherical 3-manifold. This yields a new, homological proof of a classical
theorem of Stallings: if $G = \pi_1(M^3)$ is the fundamental group of a compact
irreducible 3-manifold $M^3$ and $\phi \colon G \to \mathbb{Z}$ is a surjective
homomorphism with finitely generated kernel, then $\phi$ is induced by a
topological fibration of $M^3$ over the circle.
