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 on orientable geometrizable 3-manifolds, all ${\pi }_1$ of (geometrizable) 3-manifolds have a solvable conjugacy problem. In corollaries, both the twisted conjugacy problem in closed surface groups and the conjugacy problem in closed surface-by-cyclic groups, are solvable.

arXiv comment40 pages. 8 figures. Improved version of arXiv.math.GR/0512484 (2011). To appear