Obstruction theory on 8-manifolds

Cadek, Martin; Crabb, Michael; Vanzura, Jiri

Obstruction theory on 8-manifolds

Authors

Cadek, Martin

Crabb, Michael

Vanzura, Jiri

Description

This note 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 critera for the existence of almost complex and almost quaternionic structures on the tangent bundle and for the reduction of the structure group to U(3) by the homomorphism U(3) --> O(8) given by the Lie algebra representation of PU(3).
19 pages