The membership problem for 3–manifold groups is solvable

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 is an element of pi, and determines whether or not g is an element of Gamma.