  We construct a correspondence between epimorphisms $\varphi \colon \pi_1(M)
\to F_r$ from the fundamental group of a compact manifold $M$ onto the free
group of rank $r$, and systems of $r$ framed non-separating hypersurfaces in
$M$, which induces a bijection onto framed cobordism classes of such systems.
In consequence, for closed manifolds any such $\varphi$ can be represented by
the Reeb epimorphism of a Morse function $f\colon M \to \mathbb{R}$, i.e. by
the epimorphism induced by the quotient map $M \to \mathcal{R}(f)$ onto the
Reeb graph of $f$. Applying this construction we discuss the problem of
classification up to (strong) equivalence of epimorphisms onto free groups,
providing a new purely geometrical-topological proof of the solution of this
problem for surface groups.
