Differential geometric invariants for time-reversal symmetric Bloch-bundles II: The low dimensional "Quaternionic" case

Abstract

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.