Obstruction theory on 8-manifolds

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Authors	ČADEK Martin CRABB Michael VANŽURA Jiří
Year of publication	2008
Type	Article in Periodical
Magazine / Source	Manuscripta Mathematica
MU Faculty or unit	Faculty of Science
Citation
Web	http://www.springerlink.com/content/km887775657x4821/?p=c8e1189214394ca5aa586ba53e457947&pi=2
Field	General mathematics
Keywords	Reduction of the structure group; complex structure; quaternionic structure
Description	This paper gives a uniform, self-contained, and fairly direct approach to a variety of obstruction-theoretic problems on 8-manifolds. It gives necessary and sufficient cohomological criteria for the existence of complex and quaternionic structures on eight-dimensional vector bundles and for the reduction of the structure group of such bundles to U(3) by the homomorphism from U(3) to O(8) given by the Lie algebra representation of PU(3).
Related projects:	Mathematical structures and their physical applications