  We derive the dynamics of the gravitational collapse of a homogeneous and
spherically symmetric cloud in a classical set-up endowed with a topological
sector of gravity and a non-minimal coupling to fermions. The effective theory
consists of the Einstein-Hilbert action plus Dirac fermions interacting through
a four-fermion vertex. At the classical level, we obtain the same picture that
has been recently studied by some of us within a wide range of effective
theories inspired by a super-renormalizable and asymptotically free theory of
gravity. The classical singularity is replaced by a bounce, beyond which the
cloud re-expands indefinitely. We thus show that, even at a classical level, if
we allow for a non-minimal coupling of gravity to fermions, event horizons may
never form for a suitable choice of some parameters of the theory.
