  Tsuboi proved that the Calabi invariant of the closed disk transgresses to
the Euler class of foliated circle bundles and suggested looking for its
higher-dimensional analog. In this paper, we construct a cohomology class of
the group of volume-preserving diffeomorphisms of a real-cohomologically
acyclic manifold with sphere boundary, which is closely related to McDuff's
secondary class, and prove that this cohomology class transgresses to the Euler
class of foliated sphere bundles.
