Pro-$p$ completions of $P{D}_n$-groups

Abstract

We sharpen earlier work on the pro-$p$ completions of orientable $P{D}_3$-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 $P{D}_n$ groups for $n\le 5$, including surface-by-surface groups.

Some of the results of the final section are based on arXiv 1305.3953 [math.GT]