## Multy-Dimensional Theory of Gravity-Electro Interactions, Time Machine and Foliations

### Guts, Alexander K.

American Physical Society, APS/AAPT Joint Meeting, May 2-5, 1996, abstract #J15.02

The space-time V^4 can be considered as a leaf of foliation \cal F
of codimision q, q>= 1 in Lorentzian manifold V^{4+q}.
In some cases the leaf V^4 infinitely winds round (wraps)
itself and so the Past or Future lies in any small neighbourhood
(in topology of V^{4+q}) of the Present. This leaf is called spring
leaf. We can transfer to the such near Past throught
the 4-dimensional wormhole along timelike geodesic in V^{4+q}
(A.K.Guts, Izvestija VUZov. Fizika (Russian), N 2 (1996) ).

How will it understand that our space-time is the spring leaf?
The 6-dimensional theory of
gravity-electro-weak interactions (Ju.S.Vladimirov,
Dimension of physical space-time and union of interactions.
-- Moscow state univ., 1987. ) connects the vector fields
A_\mu and Z_\mu (\mu=0,1,2,3) with differential 1-forms
\lambda=\lambda_Adx^A and \sigma=\sigma_Adx^A (A=0,1,2,3,5,6),
where G_AB=g_AB-\lambda_A\lambda_B -\sigma_A\sigma_B is
the metric of V^6 and g_AB is metric of V^4. The 1-forms
\lambda, \sigma define the characteristic classes of foliation
\cal F.

The calculation of these cohomological classes gives
the answer to the question.
For example under q=1 there exists only one such
class GV(\cal F) that is called the Godbillon-Vey class,
and if GV(\cal F)neq 0 then \cal F has a spring leaf.
Hence the investigation of electro-weak interactions allows
to solve some principal questions that concerns to Time machine.