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,

Cambridge,

United Kingdom.

mailto:G.Wilkes@dpmms.cam.ac.uk






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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