  We introduce basic characteristic classes and numbers as new invariants for
Riemannian foliations. If the ambient Riemannian manifold M is simply connected
(or more generally if the foliation is a transversely orientable Killing
foliation), if M is complete and if the space of leaf closures is compact, then
the basic characteristic numbers are determined by the infinitesimal dynamical
behavior of the foliation at the union of its closed leaves. In fact, they can
be computed with an Atiyah-Bott-Berline-Vergne-type integration formula for
equivariant basic cohomology.
