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Distinguishing geometries using finite quotients
(Mathematical Sciences PublishersGeometry and Topology, 2017-02-10)
We prove that the profinite completion of the fundamental group of a compact 3-manifold M satisfies a Tits alternative: if a closed subgroup H does not contain a free pro-p subgroup for any p, then H is virtually soluble, ...
Pro-p subgroups of profinite completions of 3-manifold groups
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 ...