An aspherical 5-manifold with perfect fundamental group

TL;DR

This paper constructs specific 5-dimensional aspherical manifolds with perfect fundamental groups, advancing the understanding of Poincaré duality groups and their properties.

Contribution

It provides the first known examples of aspherical closed orientable 5-manifolds with perfect fundamental groups, addressing open questions in the topology of Poincaré duality groups.

Findings

Constructed aspherical 5-manifolds with perfect fundamental groups.

Addressed the existence of examples with 'dimension drop' 1.

Contributed to the classification of PD_n-groups with certain pro-p properties.

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 $PD_n$-groups with pro-$p$ completion a pro-$p$ Poincar\'e duality group of dimension $\leq{n-2}$. We also consider the question of whether there are any examples with "dimension drop" 1.