The conjugacy problem in groups of non-orientable 3-manifolds
  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. 
Jean-Philippe Pr\'eaux
math.GR math.AT math.GT