Obstruction theory on 8-manifolds

This paper gives a uniform, self-contained, and fairly direct approach to a variety of obstruction-theoretic problems on 8-manifolds. We give necessary and sufficient cohomological criteria for the existence of complex and quaternionic structures on eight-dimensional vector bundles and for the reduc...

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Bibliographic Details
Published in:Manuscripta mathematica 2008-10, Vol.127 (2), p.167-186
Main Authors: Čadek, Martin, Crabb, Michael, Vanžura, Jiří
Format: Article
Language:English
Subjects:
Algebraic Geometry
Calculus of Variations and Optimal Control
Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
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Summary:This paper gives a uniform, self-contained, and fairly direct approach to a variety of obstruction-theoretic problems on 8-manifolds. We give 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 U(3) → O(8) given by the Lie algebra representation of PU(3).
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-008-0203-x