ON Sp(2) AND Sp(2) · Sp(1)-STRUCTURES IN 8-DIMENSIONAL VECTOR BUNDLES

Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to Sp(2) or Sp(2) · Sp(1) if and only if the vector bundle associated to ξ via a certain outer automorphism of the group Spin(8) has 3 linearly independent sections or contains a 3-dimension...

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Bibliographic Details
Published in:Publicacions matemàtiques 1997-01, Vol.41 (2), p.383-401
Main Authors: Cadek, Martin, Vanzura, Jirí
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Clases características
Cuaterniones
Fibrados
Homomorphisms
Mathematical manifolds
Mathematical vectors
Signatures
Subalgebras
Sufficient conditions
Tangents
Variedad cerrada
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Summary:Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to Sp(2) or Sp(2) · Sp(1) if and only if the vector bundle associated to ξ via a certain outer automorphism of the group Spin(8) has 3 linearly independent sections or contains a 3-dimensional subbundle. Necessary and sufficient conditions for the existence of an Sp(2)-structure in ξ over a closed connected spin manifold of dimension 8 are also given in terms of characteristic classes.
ISSN:0214-1493
2014-4350