Groups, Geometry, and Dynamics


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Volume 10, Issue 1, 2016, pp. 473–522
DOI: 10.4171/GGD/354

Published online: 2016-02-09

The conjugacy problem in groups of non-orientable 3-manifolds

Jean-Philippe Préaux[1]

(1) Aix-Marseille Université, Marseille, France

We prove that fundamental groups of non-orientable 3-manifolds have a solvable conjugacy problem and construct an algorithm. Together with our earlier work on the conjugacy problem in groups of orientable geometrisable 3-manifolds, all 1 of (geometrisable) 3-manifolds have a solvable conjugacy problem. As corollaries, both the twisted conjugacy problem in closed surface groups and the conjugacy problem in closed surface-by-cyclic groups, are solvable.

Keywords: Conjugacy problem, fundamental group, non-orientable 3-manifolds, topological decomposition of 3-manifolds, graphs of groups

Préaux Jean-Philippe: The conjugacy problem in groups of non-orientable 3-manifolds. Groups Geom. Dyn. 10 (2016), 473-522. doi: 10.4171/GGD/354