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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Research of M. Čadek supported by the grant MSM 0021622409 of the Czech Ministry of Education. Research of J. Vanžura supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan AVOZ10190503, and by the grant 201/05/2117 of the Grant Agency of the Czech Republic.
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Čadek, M., Crabb, M. & Vanžura, J. Obstruction theory on 8-manifolds. manuscripta math. 127, 167–186 (2008). https://doi.org/10.1007/s00229-008-0203-x
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DOI: https://doi.org/10.1007/s00229-008-0203-x