An aspherical 5-manifold with perfect fundamental group

J.A.Hillman

Abstract

We construct aspherical closed orientable 5-manifolds with perfect fundamental group. This completes part of our study (with D.H.Kochloukova and I.Lima) of $P{D}_n$-groups with pro-$p$ completion a pro-$p$ Poincaré duality group of dimension $\le n-2$. We also consider the question of whether there are any examples with "dimension drop" 1.

Keywords: aspherical; pro-$p$ completion;Poincaré duality group.