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Quaternionic structures |
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| Authors: | Martin ?adek Michael Crabb |
| Institution: | a Department of Mathematics, Masaryk University, Kotlá?ská 2, 611 37 Brno, Czech Republic b Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, UK c Academy of Sciences of the Czech Republic, Institute of Mathematics, ?i?kova 22, 616 62 Brno, Czech Republic |
| Abstract: | 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 Spinc manifolds in ?adek et al. (2008) 5] and may be of some interest, also, in quaternionic and algebraic geometry. |
| Keywords: | Bundles of quaternionic algebras Almost quaternionic manifolds Vector bundles Characteristic classes K-theory Morita equivalence |
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