  In this paper we show that there exists a new class of topological field
theories, whose correlators are intersection numbers of cohomology classes in a
constrained moduli space. Our specific example is a formulation of 2D
topological gravity. The constrained moduli-space is the Poincare' dual of the
top Chern-class of the bundle $E_\rightarrow {\cal M}_g$, whose sections are
the holomorphic differentials. Its complex dimension is $2g-3$, rather then
$3g-3$. We derive our model by performing the A-topological twist of N=2
supergravity, that we identify with N=2 Liouville theory, whose rheonomic
construction is also presented. The peculiar field theoretical mechanism,
rooted in BRST cohomology, that is responsible for the constraint on moduli
space is discussed, the key point being the fact that the graviphoton becomes a
Lagrange multiplier after twist. The relation with conformal field theories is
also explored. Our formulation of N=2 Liouville theory leads to a
representation of the N=2 superconformal algebra with $c=6$, instead of the
value $c=9$ that is obtained by untwisting the Verlinde and Verlinde
formulation of topological gravity. The reduced central charge is the shadow,
in conformal field theory, of the constraint on moduli space.
