On Sp(2) and Sp(2) ·Sp(1)-structures in 8-dimensional vector bundles

Autores: Martin Cadek, Jirí Vanzura
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 41, Nº 2, 1997, págs. 383-401
Idioma: inglés
DOI: 10.5565/publmat_41297_05
Títulos paralelos:
- Estructuras Sp(2) y Sp(2) · Sp(1) en un fibrado de vectores 8-dimensional
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Resumen
- Let $\xi$ be an oriented 8-dimensional vector bundle. We prove that the structure group $SO(8)$ of $\xi$ can be reduced to $Sp(2)$ or $Sp(2)\cdot Sp(1)$ if and only if the vector bundle associated to $\xi$ 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 $\xi$ over a closed connected spin manifold of dimension~$8$ are also given in terms of characteristic classes.