Profinite Completions, Cohomology and JSJ Decompositions of Compact 3-Manifolds


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New Zealand Journal of Mathematics

Vol. 48, (2018), Pages 101-113

Gareth Wilkes

Department of Pure Mathematics and Mathematical Statistics,

Centre for Mathematical Sciences,

University of Cambridge,

Wilberforce Road,


United Kingdom.

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 group pairs on profinite trees.

Keywords 3-manifold; profinite completion; cohomology.

Classification (MSC2000) 57M05, 57M27, 20E18, 20J06.

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