Pro-$p$ subgroups of profinite completions of 3-manifold groups

Abstract

We completely describe the finitely generated pro-$p$ subgroups of the profinite completion of the fundamental group of an arbitrary $3$-manifold. We also prove a pro-$p$ analogue of the main theorem of Bass--Serre theory for finitely generated pro-$p$ groups.

26 pages, no figures. v2 corrects an error in the proof of the main theorem. This is the final version accepted for publication

References in corpus (2)

• Distinguishing geometries using finite quotients
• Subgroup properties of pro-p extensions of centralizers

Cited by in corpus (4)

• On profinite rigidity amongst free-by-cyclic groups I: the generic case
• Profinite almost rigidity in 3-manifolds
• Prosoluble subgroups of the profinite completion of the fundamental group of compact 3-manifolds
• Subgroups of pro-$p$ ${\mathrm{PD}}^3$-groups