An aspherical 5-manifold with perfect fundamental group · arXivDesk
1305.3953May 16, 2013First 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
An aspherical 5-manifold with perfect fundamental group
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 PDn-groups with pro-p completion a pro-p Poincaré duality group of dimension ≤n−2
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. We also consider the question of whether there are any examples with "dimension drop" 1.