  A quantum model of universe is constructed in which values of dimensionless
coupling constants of the fundamental interactions (including the cosmological
constant) are determined via certain topological invariants of manifolds
forming finite ensembles of 3D Seifert fibrations. The characteristic values of
the coupling constants are explicitly calculated as the set of rational numbers
(up to the factor $2\pi$) on the basis of a hypothesis that these values are
proportional to the mean relative fluctuations of discrete volumes of manifolds
in these ensembles. The discrete volumes are calculated using the standard
Alexandroff procedure of constructing $T_0$-discrete spaces realized as nerves
corresponding to characteristic canonical triangulations which are compatible
with the Milnor representation of Seifert fibered homology spheres being the
building material of all used 3D manifolds. Moreover, the determination of all
involved homology spheres is based on the first nine prime numbers ($p_1=2,
>..., p_9=23$). The obtained hierarchy of coupling constants at the present
evolution stage of universe well reproduces the actual hierarchy of the
experimentally observed dimensionless low-energy coupling constants.
