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The membership problem for $3$–manifold groups is solvable

Stefan Friedl and Henry Wilton

Algebraic & Geometric Topology 16 (2016) 1827–1850

We show that the membership problem for finitely generated subgroups of 3–manifold groups is uniformly solvable. That is, there is an algorithm that takes as input a presentation for the fundamental group π of a compact 3–manifold, a finite generating set for a subgroup Γ, and an element g π, and determines whether or not g Γ.

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3–manifolds, membership problem for subgroups
Mathematical Subject Classification 2010
Primary: 20E26, 57M05
Received: 14 February 2014
Revised: 26 November 2015
Accepted: 6 December 2015
Published: 12 September 2016
Stefan Friedl
Fakultät für Mathematik
Universität Regensburg
D-93053 Regensburg
Henry Wilton
Cambridge University
Centre for Mathematical Sciences
Wilberforce Road
United Kingdom