  We propose a generalization of the collective field theory hamiltonian,
including interactions between the original bosonic collective field $w_0 (z)$
and supplementary fields ${\bar w}_j (z)$ realizing classically a $w_\infty$
algebra. The latter are then shown to represent a 3--dimensional topological
field theory. This generalization follows from a conjectured representation of
the $W_{1 + \infty}$ algebra of bilinear fermion operators underlying the
original matrix model. It provides an improved bosonization scheme for $1+1$
dimensional fermion theories.
