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 invariants able to distinguish between inequivalent realizations of “quaternionic” structures. This is a nontrivial generalization of results previously known only in the case of tori with time-reversal involution.