Quaternionic structures

Any oriented 4-dimensional real vector bundle is naturally a line bundle over a bundle of quaternion algebras. In this paper we give an account of modules over bundles of quaternion algebras, discussing Morita equivalence, characteristic classes and K-theory. The results have been used to describe o...

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Bibliographic Details
Published in:Topology and its applications 2010-12, Vol.157 (18), p.2850-2863
Main Authors: Čadek, Martin, Crabb, Michael, Vanžura, Jiří
Format: Article
Language:English
Subjects:
Almost quaternionic manifolds
Bundles of quaternionic algebras
Characteristic classes
K-theory
Morita equivalence
Vector bundles
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Summary:Any oriented 4-dimensional real vector bundle is naturally a line bundle over a bundle of quaternion algebras. In this paper we give an account of modules over bundles of quaternion algebras, discussing Morita equivalence, characteristic classes and K-theory. The results have been used to describe obstructions for the existence of almost quaternionic structures on 8-dimensional Spin c manifolds in Čadek et al. (2008) [5] and may be of some interest, also, in quaternionic and algebraic geometry.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2010.09.005