The membership problem for 3–manifold groups is solvable

Friedl, Stefan¹ ; Wilton, Henry²

¹Fakultät für Mathematik, Universität Regensburg, D-93053 Regensburg, Germany
²DPMMS, Cambridge University, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom

Algebraic and Geometric Topology, Tome 16 (2016) no. 4, pp. 1827-1850

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.1827

Classification : 20E26, 57M05
Keywords: 3–manifolds, membership problem for subgroups

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