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

Keywords: aspherical; pro-\(p\) completion;Poincaré duality group.

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Friday, May 24, 2013