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

Research paper by Giuseppe De Nittis, Kiyonori Gomi

Indexed on: 13 Sep '18Published on: 13 Sep '18Published in: arXiv - Mathematical Physics



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.