Jiří Vanžura

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 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).

Various structures in 8-dimensional vector bundles over 8-manifolds

The paper is an overview of our results concerning the existence of various structures, especially complex and quaternionic, in 8-dimensional vector bundles over closed connected smooth 8-manifolds.