Obstruction theory on 8-manifolds

Details Obstruction theory on 8-manifolds Obstruction theory on 8-manifolds

2007-10-03

arxiv.org/abs/0710.0734v1

manuscripta math. 127 (2008), 167-186

Mathematics

Algebraic Topology

19 pages

Scientific paper

10.1007/s00229-008-0203-x

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).

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