  We give a geometrical set up for the semiclassical approximation to euclidean
field theories having families of minima (instantons) parametrized by suitable
moduli spaces ${\cal M}$. The standard examples are of course Yang-Mills theory
and non-linear $\sigma$-models. The relevant space here is a family of measure
spaces $\tilde {\cal N} \ra {\cal M}$, with standard fibre a distribution
space, given by a suitable extension of the normal bundle to ${\cal M}$ in the
space of smooth fields. Over $\tilde {\cal N}$ there is a probability measure
$d\mu$ given by the twisted product of the (normalized) volume element on
${\cal M}$ and the family of gaussian measures with covariance given by the
tree propagator $C_\phi$ in the background of an instanton $\phi \in {\cal M}$.
The space of ``observables", i.e. measurable functions on ($\tilde {\cal N}, \,
d\mu$), is studied and it is shown to contain a topological sector,
corresponding to the intersection theory on ${\cal M}$. The expectation value
of these topological ``observables" does not depend on the covariance; it is
therefore exact at all orders in perturbation theory and can moreover be
computed in the topological regime by setting the covariance to zero.
