  The following mechanism of action of Time machine is considered. Let
space-time $<V^4, g_{ik}>$ be a leaf of a foliation F of codimension 1 in
5-dimensional Lorentz manifold $<V^5, G_{AB}>$. If the Godbillon-Vey class
$GV(F) \neq 0$ then the foliation F has resilient leaves. Let $V^4$ be a
resilient leaf. Hence there exists an arbitrarily small neighborhood $U_a
\subset V^5$ of the event $a \in V^4$ such that $U_a \cap V^4$ consists of at
least two connected components $U_a^1$ and $U_a^2$.
  Remove the four-dimensional balls $B_a\subset U_a^1, B_b\subset U_a^2$, where
an event $b\in U_a^2$, and join the boundaries of formed two holes by means of
4-dimensional cylinder. As result we have a four-dimensional wormhole C, which
is a Time machine if b belongs to the past of event a. The past of a is lying
arbitrarily nearly. The distant Past is more accessible than the near Past. It
seems that real global space-time V^4 is a resilient one, i.e. is a resilient
leaf of some foliation F.
  It follows from the conformal Kaluza-Klein theory that the movement to the
Past through four-dimensional wormhole C along geodesic with respect to metric
G_{AB} requires for time machine of large energy and electric charge.

General Relativity and Quantum Cosmology