## 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.

: Primary 20Jxx.

This paper is available as a pdf (220kB) file. It is also on the arXiv: arxiv.org/abs/2205.06155.

 Tuesday, May 31, 2022