Letters in Mathematical Physics

, Volume 108, Issue 5, pp 1225–1277 | Cite as

The FKMM-invariant in low dimension

Article

Abstract

In this paper, we investigate the problem of the cohomological classification of “Quaternionic” vector bundles in low dimension (\(d\leqslant 3\)). We show that there exists a characteristic class \(\kappa \), 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 \(\kappa \).

Keywords

“Quaternionic” vector bundles FKMM-invariant Characteristic classes Topological quantum systems 

Mathematics Subject Classification

Primary 57R22 Secondary 53A55 55N25 53C80 

Notes

Acknowledgements

GD’s research is supported by the Grant Iniciación en Investigación 2015—No. 11150143 funded by FONDECYT. KG’s research is supported by the JSPS KAKENHI Grant No. 15K04871.

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Authors and Affiliations

  1. 1.Facultad de Matemáticas and Instituto de FísicaPontificia Universidad CatólicaSantiagoChile
  2. 2.Department of Mathematical SciencesShinshu UniversityNaganoJapan

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