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Profinite detection of 3-manifold decompositions

Part of: Structure and classification of infinite or finite groups Low-dimensional topology Topological manifolds

Published online by Cambridge University Press:  07 January 2019

Henry Wilton Open the ORCID record for Henry Wilton [Opens in a new window]  and
Pavel Zalesskii Open the ORCID record for Pavel Zalesskii [Opens in a new window]
Henry Wilton
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK email hjrw2@cam.ac.uk
Pavel Zalesskii
Affiliation:
Department of Mathematics, University of Brasília, 70910-9000 Brasília, Brazil email pz@mat.unb.br
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Abstract

The profinite completion of the fundamental group of a closed, orientable $3$-manifold determines the Kneser–Milnor decomposition. If $M$ is irreducible, then the profinite completion determines the Jaco–Shalen–Johannson decomposition of $M$.

Keywords

3-manifoldsprofinite completionsJaco–Shalen–Johannson decompositions

MSC classification

Primary: 57N10: Topology of general $3$-manifolds
Secondary: 20E26: Residual properties and generalizations; residually finite groups 57M05: Fundamental group, presentations, free differential calculus
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 2 , February 2019 , pp. 246 - 259
Copyright
© The Authors 2019 

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