The FKMM-invariant in low dimension

Abstract

In this paper we investigate the problem of the cohomological classification of "Quaternionic" vector bundles in low-dimension ($d⩽3$). We show that there exists a characteristic classes $\kappa$, called the FKMM-invariant, which takes value in the relative equivariant Borel cohomology and completely classifies "Quaternionic" vector bundles in low-dimension. The main subject of the paper concerns a discussion about the surjectivity of $\kappa$.

38 pages. Keywords: "Quaternionic" vector bundles, FKMM-invariant, Characteristic classes, Topological quantum systems. arXiv admin note: text overlap with arXiv:1603.09421

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• Differential geometric invariants for time-reversal symmetric Bloch-bundles II: The low dimensional "Quaternionic" case
• Topological Insulators and the Kane-Mele Invariant: Obstruction and Localisation Theory
• A new light on the FKMM invariant and its consequences