pro-\(p\) completions of \(PD_n\)-groups

J.A.Hillman and D.H.Kochloukova

Abstract

We sharpen earlier work on the pro-\(p\) completions of orientable \(PD_3\)-groups. There are four cases, and we give examples of aspherical 3-manifolds representing each case. In three of the four cases the new results are best possible. We also consider the pro-\(p\) completion of some orientable \(PD_n\) groups for \(n \leq 5\), including surface-by-surface groups.

Keywords: pro-\(p\) completion, \(PD_3\)-group, \(PD_n\)-group, surface bundle.

AMS Subject Classification: Primary 20Jxx.