Pro-$p$ completions of $PD_n$-groups

Jonathan Hillman; Dessislava H. Kochloukova

Pro-$p$ completions of $PD_n$-groups

Geometric Topology 2022-05-13 v1 Group Theory

Authors: Jonathan Hillman , Dessislava 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_n-groups orientable pd_3-groups aspherical 3-manifolds surface-by-surface groups condition number

Cite

@article{arxiv.2205.06155,
  title  = {Pro-$p$ completions of $PD_n$-groups},
  author = {Jonathan Hillman and Dessislava H. Kochloukova},
  journal= {arXiv preprint arXiv:2205.06155},
  year   = {2022}
}

Comments

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

Pro-$p$ completions of $PD_n$-groups

Abstract

Keywords

Cite

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