  We show that a regular isomorphism of profinite completion of the fundamental
groups of two 3-manifolds $N_1$ and $N_2$ induces an isometry of the Thurston
norms and a bijection between the fibered classes. We study to what extent does
the profinite completion of knot groups distinguish knots and show that it
distinguishes each torus knot and the figure eight knot among all knots. We
show also that it distinguishes between hyperbolic knots with cyclically
commensurable complements under the assumption that their Alexander polynomials
have at least one zero which is not a root of unity.
