  By using the explicit knowledge of the lowest energy single particle wave
functions in the presence of an {\it arbitrary} magnetic field, we extend to
the case of a torus Jain's idea of looking at the FQHE as a manifestation of an
integer effect for {\it composite fermions}. We show that this can be realized
thanks to a redefinition of the vacuum state that is explicitly collective in
nature. We also discuss the relationship of this approach with the hierarchical
scheme and with the characterization of the Hall states in terms of
$W_{1+\infty}$ algebras and 2D conformal field theories.
