  We study 2-d $\phi F$ gauge theories with the objective to understand, also
at the quantum level, the emergence of induced gravity. The wave functionals -
representing the eigenstates of a vanishing flat potential - are obtained in
the $\phi$ representation. The composition of the space they describe is then
analyzed: the state corresponding to the singlet representation of the gauge
group describes a topological universe. For other representations a metric
which is invariant under the residual gauge group is induced, apart from
possible topological obstructions. Being inherited from the group metric it is
rather rigid.
