Conjugacy problem in groups of oriented geometrizable 3-manifolds

The aim of this paper is to show that the fundamental group of an oriented 3-manifold which satisfies Thurstonʹs geometrization conjecture has a solvable conjugacy problem. In other words, for any such 3-manifold M, there exists an algorithm which can decide for any couple of elements u , v of π 1 ( M ) whether u and v are in the same conjugacy class of π 1 ( M ) or not. More topologically, the algorithm decides for any two loops in M, whether they are freely homotopic or not.