#### Volume 16, issue 4 (2016)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
The membership problem for $3$–manifold groups is solvable

### Stefan Friedl and Henry Wilton

Algebraic & Geometric Topology 16 (2016) 1827–1850
##### 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 $\pi$ of a compact 3–manifold, a finite generating set for a subgroup $\Gamma$, and an element $g\in \pi$, and determines whether or not $g\in \Gamma$.

##### Keywords
3–manifolds, membership problem for subgroups
##### Mathematical Subject Classification 2010
Primary: 20E26, 57M05