  A cosmological model connecting the evolution of universe with a sequence of
topology changes described by a collection of specific graph cobordisms, is
constructed. It is shown that an adequate topological field theory (of BF-type)
can be put into relation to each graph cobordism. The explicit expressions for
transition amplitudes (partition functions) are written in these BF-models and
it is shown that the basic topological invariants of the graph cobordisms
(intersection matrices) play the r{\^o}le of coupling constants between the
formal analogues of electric and magnetic fluxes quantized {\`a} la Dirac, but
with the use of Poicar{\'e}--Lefschetz duality. For a specific graph cobordism,
the diagonal elements and eigenvalues of the intersection matrix reproduce the
hierarchy of dimensionless low-energy coupling constants of the fundamental
interactions acting in the real universe.
