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

Abstract

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.