Product rigidity (Ex)
From Manifold Atlas
Let be a group satisfying the Full Farrell-Jones Conjecture. Let be a closed aspherical manifold with fundamental group . Suppose that , where the cohomological dimension of both and is different from and . Show that is homeomorphic to a product of two closed aspherical manifolds with for .
Hint: Use the fact that and are Poincaré duality groups, if is a Poincar\'e duality group.