Obstruction theory on 8-manifolds

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 reducti...

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Bibliographic Details
Published in:arXiv.org 2007-10
Main Authors: Cadek, Martin, Crabb, Michael, Vanzura, Jiri
Format: Article
Language:English
Subjects:
Homomorphisms
Lie groups
Manifolds
Online Access:Get full text
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Summary: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).
ISSN:2331-8422
DOI:10.48550/arxiv.0710.0734