  This paper is devoted to the construction of differential geometric
invariants for the classification of "Quaternionic" vector bundles. Provided
that the base space is a smooth manifold of dimension two or three endowed with
an involution that leaves fixed only a finite number of points, it is possible
to prove that the Wess-Zumino term and the Chern-Simons invariant yield
topological quantities able to distinguish between inequivalent realization of
"Quaternionic" structures.
