An aspherical 5-manifold with perfect fundamental group
Geometric Topology
2026-05-15 v3 Group Theory
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 -groups with pro- completion a pro- Poincar\'e duality group of dimension . We also consider the question of whether there are any examples with "dimension drop" 1.
Keywords
Cite
@article{arxiv.1305.3953,
title = {An aspherical 5-manifold with perfect fundamental group},
author = {J. A. Hillman},
journal= {arXiv preprint arXiv:1305.3953},
year = {2026}
}
Comments
First theorem split into two, and question raised as to alternative sources of examples. Result on dimension drop 1 strengthened, to exclude Demushkin groups as pro-$p$ completions of $PD_3$-groups