Abstract

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).

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