Profinite completions, cohomology and JSJ decompositions of compact 3-manifolds

Gareth Wilkes

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arXiv · 1802.09282

Profinite completions, cohomology and JSJ decompositions of compact 3-manifolds

Gareth Wilkes

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Abstract

In this paper we extend previous results concerning the behaviour of JSJ decompositions of closed 3-manifolds with respect to the profinite completion to the case of compact 3-manifolds with boundary. We also illustrate an alternative and perhaps more natural approach to part of the original theorem, using relative cohomology to analyse the actions of an-annular atoroidal groups on profinite trees.

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Gareth Wilkes. 2018-02-26. Profinite completions, cohomology and JSJ decompositions of compact 3-manifolds. https://arxiv.org/abs/1802.09282

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