The membership problem for 3–manifold groups is solvable

Friedl, Stefan; Wilton, Henry

doi:10.2140/agt.2016.16.1827

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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

DOI: 10.2140/agt.2016.16.1827

Abstract

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 $g \in π$ , and determines whether or not $g \in Γ$ .

Keywords

3–manifolds, membership problem for subgroups

Mathematical Subject Classification 2010

Primary: 20E26, 57M05

References

Publication

Received: 14 February 2014

Revised: 26 November 2015

Accepted: 6 December 2015

Published: 12 September 2016

Authors

Stefan Friedl
Fakultät für Mathematik Universität Regensburg D-93053 Regensburg Germany

Henry Wilton
DPMMS Cambridge University Centre for Mathematical Sciences Wilberforce Road Cambridge CB3 0WB United Kingdom

Volume 16, issue 4 (2016)