The characterization of Poincaré duality groups by manifold groups

A finitely presented group $G$ is an $n$-dimensional Poincaré duality group when its group cohomology satisfies Poincaré duality in dimension $n$. Poincaré duality groups conjecture. A finitely presented group is an $n$-dimensional Poincaré duality group if and only if it is the fundamental group of a closed $n$-dimensional topological manifold. This would characterize manifold groups algebraically through group-theoretic Poincaré duality.