## 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 $$PD_n$$-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